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Cobordism

In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary (French bord, giving cobordism) of a manifold. Two manifolds of the same dimension are cobordant if their disjoint union is the boundary of a compact manifold one dimension higher.

The boundary of an (n + 1)-dimensional manifold W is an n-dimensional manifold ∂W that is closed, i.e., with empty boundary. In general, a closed manifold need not be a boundary: cobordism theory is the study of the difference between all closed manifolds and those that are boundaries. The theory was originally developed by René Thom for smooth manifolds (i.e., differentiable), but there are now also versions for piecewise linear and topological manifolds.

A cobordism between manifolds M and N is a compact manifold W whose boundary is the disjoint union of M and N, $$\partial W=M \sqcup N$$.

Cobordisms are studied both for the equivalence relation that they generate, and as objects in their own right. Cobordism is a much coarser equivalence relation than diffeomorphism or homeomorphism of manifolds, and is significantly easier to study and compute. It is not possible to classify manifolds up to diffeomorphism or homeomorphism in dimensions ≥ 4 – because the word problem for groups cannot be solved – but it is possible to classify manifolds up to cobordism. Cobordisms are central objects of study in geometric topology and algebraic topology. In geometric topology, cobordisms are intimately connected with Morse theory, and h-cobordisms are fundamental in the study of high-dimensional manifolds, namely surgery theory. In algebraic topology, cobordism theories are fundamental extraordinary cohomology theories, and categories of cobordisms are the domains of topological quantum field theories.

Manifolds
Roughly speaking, an n-dimensional manifold M is a topological space locally (i.e., near each point) homeomorphic to an open subset of Euclidean space $$\R^n.$$ A manifold with boundary is similar, except that a point of M is allowed to have a neighborhood that is homeomorphic to an open subset of the half-space

 * $$\{(x_1,\ldots,x_n) \in \R^n \mid x_n \geqslant 0\}.$$

Those points without a neighborhood homeomorphic to an open subset of Euclidean space are the boundary points of $$M$$; the boundary of $$M$$ is denoted by $$\partial M$$. Finally, a closed manifold is, by definition, a compact manifold without boundary ($$\partial M=\emptyset$$.)

Cobordisms
An $$(n+1)$$-dimensional cobordism is a quintuple $$(W; M, N, i, j)$$ consisting of an $$(n+1)$$-dimensional compact differentiable manifold with boundary, $$W$$; closed $$n$$-manifolds  $$M$$, $$N$$; and embeddings $$i\colon M \hookrightarrow \partial W$$, $$j\colon N \hookrightarrow\partial W$$ with disjoint images such that

 * $$\partial W = i(M) \sqcup j(N)~.$$

The terminology is usually abbreviated to $$(W; M, N)$$. M and N are called cobordant if such a cobordism exists. All manifolds cobordant to a fixed given manifold M form the cobordism class of M.

Every closed manifold M is the boundary of the non-compact manifold M × [0, 1); for this reason we require W to be compact in the definition of cobordism. Note however that W is not required to be connected; as a consequence, if M = ∂W1 and N = ∂W2, then M and N are cobordant.

Examples
The simplest example of a cobordism is the unit interval. It is a 1-dimensional cobordism between the 0-dimensional manifolds {0}, {1}. More generally, for any closed manifold M, (M × I; M × {0}, M × {1}) is a cobordism from M × {0} to M × {1}.

If M consists of a circle, and N of two circles, M and N together make up the boundary of a pair of pants W (see the figure at right). Thus the pair of pants is a cobordism between M and N. A simpler cobordism between M and N is given by the disjoint union of three disks.

The pair of pants is an example of a more general cobordism: for any two n-dimensional manifolds M, M′, the disjoint union $$M \sqcup M'$$ is cobordant to the connected sum $$M\mathbin{\#}M'.$$ The previous example is a particular case, since the connected sum $$\mathbb{S}^1\mathbin{\#}\mathbb{S}^1$$ is isomorphic to $$\mathbb{S}^1.$$ The connected sum $$M\mathbin{\#}M'$$ is obtained from the disjoint union $$M \sqcup M'$$ by surgery on an embedding of $$\mathbb{S}^0 \times \mathbb{D}^n$$ in $$M \sqcup M'$$, and the cobordism is the trace of the surgery.

Terminology
An n-manifold M is called null-cobordant if there is a cobordism between M and the empty manifold; in other words, if M is the entire boundary of some (n + 1)-manifold. For example, the circle is null-cobordant since it bounds a disk. More generally, a n-sphere is null-cobordant since it bounds a (n + 1)-disk. Also, every orientable surface is null-cobordant, because it is the boundary of a handlebody. On the other hand, the 2n-dimensional real projective space $$\mathbb{P}^{2n}(\R)$$ is a (compact) closed manifold that is not the boundary of a manifold, as is explained below.

The general bordism problem is to calculate the cobordism classes of manifolds subject to various conditions.

Null-cobordisms with additional structure are called fillings. Bordism and cobordism are used by some authors interchangeably; others distinguish them. When one wishes to distinguish the study of cobordism classes from the study of cobordisms as objects in their own right, one calls the equivalence question bordism of manifolds, and the study of cobordisms as objects cobordisms of manifolds.

The term bordism comes from French bord, meaning boundary. Hence bordism is the study of boundaries. Cobordism means "jointly bound", so M and N are cobordant if they jointly bound a manifold; i.e., if their disjoint union is a boundary. Further, cobordism groups form an extraordinary cohomology theory, hence the co-.

Variants
The above is the most basic form of the definition. It is also referred to as unoriented bordism. In many situations, the manifolds in question are oriented, or carry some other additional structure referred to as G-structure. This gives rise to "oriented cobordism" and "cobordism with G-structure", respectively. Under favourable technical conditions these form a graded ring called the cobordism ring $$\Omega^G_*$$, with grading by dimension, addition by disjoint union and multiplication by cartesian product. The cobordism groups $$\Omega^G_*$$ are the coefficient groups of a generalised homology theory.

When there is additional structure, the notion of cobordism must be formulated more precisely: a G-structure on W restricts to a G-structure on M and N. The basic examples are G = O for unoriented cobordism, G = SO for oriented cobordism, and G = U for complex cobordism using stably complex manifolds. Many more are detailed by Robert E. Stong.

In a similar vein, a standard tool in surgery theory is surgery on normal maps: such a process changes a normal map to another normal map within the same bordism class.

Instead of considering additional structure, it is also possible to take into account various notions of manifold, especially piecewise linear (PL) and topological manifolds. This gives rise to bordism groups $$\Omega_*^{PL}(X), \Omega_*^{TOP}(X)$$, which are harder to compute than the differentiable variants.

Surgery construction
Recall that in general, if X, Y are manifolds with boundary, then the boundary of the product manifold is ∂(X × Y) = (∂X × Y) ∪ (X × ∂Y).

Now, given a manifold M of dimension n = p + q and an embedding $$\varphi : \mathbb{S}^p \times \mathbb{D}^q \subset M,$$ define the n-manifold

 * $$N := (M - \operatorname{int~im}\varphi) \cup_{\varphi|_{\mathbb{S}^p\times \mathbb{S}^{q-1}}} \left(\mathbb{D}^{p+1}\times \mathbb{S}^{q-1}\right)$$

obtained by surgery, via cutting out the interior of $$\mathbb{S}^p \times \mathbb{D}^q$$ and gluing in $$\mathbb{D}^{p+1} \times \mathbb{S}^{q-1}$$ along their boundary

 * $$\partial \left (\mathbb{S}^p \times \mathbb{D}^q \right) = \mathbb{S}^p \times \mathbb{S}^{q-1} = \partial \left( \mathbb{D}^{p+1} \times \mathbb{S}^{q-1} \right).$$

The trace of the surgery

 * $$W := (M \times I) \cup_{\mathbb{S}^p\times \mathbb{D}^q\times \{1\}} \left(\mathbb{D}^{p+1} \times \mathbb{D}^q\right)$$

defines an elementary cobordism (W; M, N). Note that M is obtained from N by surgery on $$\mathbb{D}^{p+1}\times \mathbb{S}^{q-1} \subset N.$$ This is called reversing the surgery.

Every cobordism is a union of elementary cobordisms, by the work of Marston Morse, René Thom and John Milnor.

Examples
As per the above definition, a surgery on the circle consists of cutting out a copy of $$\mathbb{S}^0 \times \mathbb{D}^1$$ and gluing in $$\mathbb{D}^1 \times \mathbb{S}^0.$$ The pictures in Fig. 1 show that the result of doing this is either (i) $$\mathbb{S}^1$$ again, or (ii) two copies of $$\mathbb{S}^1$$

For surgery on the 2-sphere, there are more possibilities, since we can start by cutting out either $$\mathbb{S}^0 \times \mathbb{D}^2$$ or $$\mathbb{S}^1 \times \mathbb{D}^1.$$

1. $\mathbb{S}^1 \times \mathbb{D}^1$: If we remove a cylinder from the 2-sphere, we are left with two disks. We have to glue back in $\mathbb{S}^0 \times \mathbb{D}^2$ – that is, two disks - and it's clear that the result of doing so is to give us two disjoint spheres. (Fig. 2a)

2. Sphere-surgery4.png $\mathbb{S}^0 \times \mathbb{D}^2$: Having cut out two disks $\mathbb{S}^0 \times \mathbb{D}^2,$ we glue back in the cylinder $\mathbb{S}^1 \times \mathbb{D}^1.$ There are two possible outcomes, depending on whether our gluing maps have the same or opposite orientation on the two boundary circles. If the orientations are the same (Fig. 2b), the resulting manifold is the torus $\mathbb{S}^1 \times \mathbb{S}^1$ but if they are different, we obtain the Klein bottle (Fig. 2c).

Morse functions
Suppose that f is a Morse function on an (n + 1)-dimensional manifold, and suppose that c is a critical value with exactly one critical point in its preimage. If the index of this critical point is p + 1, then the level-set N := f−1(c + ε) is obtained from M := f−1(c − ε) by a p-surgery. The inverse image W := f−1([c − ε, c + ε]) defines a cobordism (W; M, N) that can be identified with the trace of this surgery.

Geometry, and the connection with Morse theory and handlebodies
Given a cobordism (W; M, N) there exists a smooth function f : W → [0, 1] such that f−1(0) = M, f−1(1) = N. By general position, one can assume f is Morse and such that all critical points occur in the interior of W. In this setting f is called a Morse function on a cobordism. The cobordism (W; M, N) is a union of the traces of a sequence of surgeries on M, one for each critical point of f. The manifold W is obtained from M × [0, 1] by attaching one handle for each critical point of f.

The Morse/Smale theorem states that for a Morse function on a cobordism, the flowlines of f′ give rise to a handle presentation of the triple (W; M, N). Conversely, given a handle decomposition of a cobordism, it comes from a suitable Morse function. In a suitably normalized setting this process gives a correspondence between handle decompositions and Morse functions on a cobordism.

History
Cobordism had its roots in the (failed) attempt by Henri Poincaré in 1895 to define homology purely in terms of manifolds. Poincaré simultaneously defined both homology and cobordism, which are not the same, in general. See Cobordism as an extraordinary cohomology theory for the relationship between bordism and homology.

Bordism was explicitly introduced by Lev Pontryagin in geometric work on manifolds. It came to prominence when René Thom showed that cobordism groups could be computed by means of homotopy theory, via the Thom complex construction. Cobordism theory became part of the apparatus of extraordinary cohomology theory, alongside K-theory. It performed an important role, historically speaking, in developments in topology in the 1950s and early 1960s, in particular in the Hirzebruch–Riemann–Roch theorem, and in the first proofs of the Atiyah–Singer index theorem.

In the 1980s the category with compact manifolds as objects and cobordisms between these as morphisms played a basic role in the Atiyah–Segal axioms for topological quantum field theory, which is an important part of quantum topology.

Categorical aspects
Cobordisms are objects of study in their own right, apart from cobordism classes. Cobordisms form a category whose objects are closed manifolds and whose morphisms are cobordisms. Roughly speaking, composition is given by gluing together cobordisms end-to-end: the composition of (W; M, N) and (W ′; N, P) is defined by gluing the right end of the first to the left end of the second, yielding (W ′ ∪N W; M, P). A cobordism is a kind of cospan: M → W ← N. The category is a dagger compact category.

A topological quantum field theory is a monoidal functor from a category of cobordisms to a category of vector spaces. That is, it is a functor whose value on a disjoint union of manifolds is equivalent to the tensor product of its values on each of the constituent manifolds.

In low dimensions, the bordism question is relatively trivial, but the category of cobordism is not. For instance, the disk bounding the circle corresponds to a nullary (0-ary) operation, while the cylinder corresponds to a 1-ary operation and the pair of pants to a binary operation.

Unoriented cobordism
The set of cobordism classes of closed unoriented n-dimensional manifolds is usually denoted by $$\mathfrak{N}_n$$ (rather than the more systematic $$\Omega_n^{\text{O}}$$); it is an abelian group with the disjoint union as operation. More specifically, if [M] and [N] denote the cobordism classes of the manifolds M and N respectively, we define $$[M]+[N] = [M \sqcup N]$$; this is a well-defined operation which turns $$\mathfrak{N}_n$$ into an abelian group. The identity element of this group is the class $$[\emptyset]$$ consisting of all closed n-manifolds which are boundaries. Further we have $$[M] + [M] = [\emptyset]$$ for every M since $$M \sqcup M = \partial (M \times [0,1])$$. Therefore, $$\mathfrak{N}_n$$ is a vector space over $$\mathbb{F}_2$$, the field with two elements. The cartesian product of manifolds defines a multiplication $$[M][N]=[M \times N],$$ so

 * $$\mathfrak{N}_* = \bigoplus_{n \geqslant 0}\mathfrak{N}_n$$

is a graded algebra, with the grading given by the dimension.

The cobordism class $$[M] \in \mathfrak{N}_n$$ of a closed unoriented n-dimensional manifold M is determined by the Stiefel–Whitney characteristic numbers of M, which depend on the stable isomorphism class of the tangent bundle. Thus if M has a stably trivial tangent bundle then $$[M]=0 \in \mathfrak{N}_n$$. In 1954 René Thom proved

 * $$\mathfrak{N}_* = \mathbb{F}_2 \left[x_i | i \geqslant 1, i \neq 2^j - 1 \right]$$

the polynomial algebra with one generator $$x_i$$ in each dimension $$i \neq 2^j - 1$$. Thus two unoriented closed n-dimensional manifolds M, N are cobordant, $$[M] = [N] \in \mathfrak{N}_n,$$ if and only if for each collection $$\left(i_1, \cdots, i_k\right)$$ of k-tuples of integers $$i \geqslant 1, i \neq 2^j - 1$$ such that $$i_1 + \cdots + i_k = n$$ the Stiefel-Whitney numbers are equal

 * $$\left\langle w_{i_1}(M) \cdots w_{i_k}(M), [M] \right\rangle = \left\langle w_{i_1}(N) \cdots w_{i_k}(N), [N] \right\rangle \in \mathbb{F}_2$$

with $$w_i(M) \in H^i\left(M; \mathbb{F}_2\right)$$ the ith Stiefel-Whitney class and $$[M] \in H_n\left(M; \mathbb{F}_2\right)$$ the $$\mathbb{F}_2$$-coefficient fundamental class.

For even i it is possible to choose $$x_i = \left[\mathbb{P}^i(\R)\right]$$, the cobordism class of the i-dimensional real projective space.

The low-dimensional unoriented cobordism groups are

 * $$\begin{align}

\mathfrak{N}_0 &= \Z/2, \\ \mathfrak{N}_1 &= 0, \\ \mathfrak{N}_2 &= \Z/2, \\ \mathfrak{N}_3 &= 0, \\ \mathfrak{N}_4 &= \Z/2 \oplus \Z/2, \\ \mathfrak{N}_5 &= \Z/2. \end{align}$$

This shows, for example, that every 3-dimensional closed manifold is the boundary of a 4-manifold (with boundary).

The Euler characteristic $$\chi(M) \in \Z$$ modulo 2 of an unoriented manifold M is an unoriented cobordism invariant. This is implied by the equation

 * $$\chi_{\partial W} = \left(1 - (-1)^{\dim W} \right)\chi_W$$

for any compact manifold with boundary $$W$$.

Therefore, $$\chi: \mathfrak{N}_i \to \Z/2$$ is a well-defined group homomorphism. For example, for any $$i_1, \cdots, i_k \in\mathbb{N}$$

 * $$\chi \left( \mathbb{P}^{2i_1} (\R) \times \cdots \times \mathbb{P}^{2i_k}(\R) \right) = 1.$$

In particular such a product of real projective spaces is not null-cobordant. The mod 2 Euler characteristic map $$\chi: \mathfrak{N}_{2i} \to \Z/2$$ is onto for all $$i \in \mathbb{N},$$ and a group isomorphism for $$i = 1.$$

Moreover, because of $$\chi(M \times N) = \chi(M)\chi(N)$$, these group homomorphism assemble into a homomorphism of graded algebras:

 * $$\begin{cases}

\mathfrak{N} \to \mathbb{F}_2[x] \\[] [M] \mapsto \chi(M) x^{\dim(M)} \end{cases}$$

Cobordism of manifolds with additional structure
Cobordism can also be defined for manifolds that have additional structure, notably an orientation. This is made formal in a general way using the notion of X-structure (or G-structure). Very briefly, the normal bundle ν of an immersion of M into a sufficiently high-dimensional Euclidean space $$\R^{n+k}$$ gives rise to a map from M to the Grassmannian, which in turn is a subspace of the classifying space of the orthogonal group: ν: M → Gr(n, n + k) → BO(k). Given a collection of spaces and maps Xk → Xk+1 with maps Xk → BO(k) (compatible with the inclusions BO(k) → BO(k+1), an X-structure is a lift of ν to a map $$\tilde \nu: M \to X_k$$. Considering only manifolds and cobordisms with X-structure gives rise to a more general notion of cobordism. In particular, Xk may be given by BG(k), where G(k) → O(k) is some group homomorphism. This is referred to as a G-structure. Examples include G = O, the orthogonal group, giving back the unoriented cobordism, but also the subgroup SO(k), giving rise to oriented cobordism, the spin group, the unitary group U(k), and the trivial group, giving rise to framed cobordism.

The resulting cobordism groups are then defined analogously to the unoriented case. They are denoted by $$\Omega^G_*$$.

Oriented cobordism
Oriented cobordism is the one of manifolds with an SO-structure. Equivalently, all manifolds need to be oriented and cobordisms (W, M, N) (also referred to as oriented cobordisms for clarity) are such that the boundary (with the induced orientations) is $$M \sqcup (-N)$$, where −N denotes N with the reversed orientation. For example, boundary of the cylinder M × I is $$M \sqcup (-M)$$: both ends have opposite orientations. It is also the correct definition in the sense of extraordinary cohomology theory.

Unlike in the unoriented cobordism group, where every element is two-torsion, 2M is not in general an oriented boundary, that is, 2[M] ≠ 0 when considered in $$\Omega_*^{\text{SO}}.$$

The oriented cobordism groups are given modulo torsion by

 * $$\Omega_*^{\text{SO}}\otimes \Q =\Q \left [y_{4i}\mid i \geqslant 1 \right ],$$

the polynomial algebra generated by the oriented cobordism classes

 * $$y_{4i}=\left [\mathbb{P}^{2i}(\Complex) \right ] \in \Omega_{4i}^{\text{SO}}$$

of the complex projective spaces (Thom, 1952). The oriented cobordism group $$\Omega_*^{\text{SO}}$$ is determined by the Stiefel–Whitney and Pontrjagin characteristic numbers (Wall, 1960). Two oriented manifolds are oriented cobordant if and only if their Stiefel–Whitney and Pontrjagin numbers are the same.

The low-dimensional oriented cobordism groups are :

 * $$\begin{align}

\Omega_0^{\text{SO}} &= \Z, \\ \Omega_1^{\text{SO}} &= 0, \\ \Omega_2^{\text{SO}} &= 0, \\ \Omega_3^{\text{SO}} &= 0, \\ \Omega_4^{\text{SO}} &= \Z, \\ \Omega_5^{\text{SO}} &= \Z_2. \end{align}$$

The signature of an oriented 4i-dimensional manifold M is defined as the signature of the intersection form on $$H^{2i}(M) \in \Z$$ and is denoted by $$\sigma(M).$$ It is an oriented cobordism invariant, which is expressed in terms of the Pontrjagin numbers by the Hirzebruch signature theorem.

For example, for any i1, ..., ik ≥ 1

 * $$\sigma \left (\mathbb{P}^{2i_1}(\Complex) \times \cdots \times \mathbb{P}^{2i_k}(\Complex) \right) = 1.$$

The signature map $$\sigma:\Omega_{4i}^{\text{SO}} \to \Z$$ is onto for all i ≥ 1, and an isomorphism for i = 1.

Cobordism as an extraordinary cohomology theory
Every vector bundle theory (real, complex etc.) has an extraordinary cohomology theory called K-theory. Similarly, every cobordism theory ΩG has an extraordinary cohomology theory, with homology ("bordism") groups $$\Omega^G_n(X)$$ and cohomology ("cobordism") groups $$\Omega^n_G(X)$$ for any space X. The generalized homology groups $$\Omega_*^G(X)$$ are covariant in X, and the generalized cohomology groups $$\Omega^*_G(X)$$ are contravariant in X. The cobordism groups defined above are, from this point of view, the homology groups of a point: $$\Omega_n^G = \Omega_n^G(\text{pt})$$. Then $$\Omega^G_n(X)$$ is the group of bordism classes of pairs (M, f) with M a closed n-dimensional manifold M (with G-structure) and f : M → X a map. Such pairs (M, f), (N, g) are bordant if there exists a G-cobordism (W; M, N) with a map h : W → X, which restricts to f on M, and to g on N.

An n-dimensional manifold M has a fundamental homology class [M] ∈ Hn(M) (with coefficients in $$\Z/2$$ in general, and in $$\Z$$ in the oriented case), defining a natural transformation

 * $$\begin{cases}

\Omega^G_n(X) \to H_n(X) \\ (M,f) \mapsto f_*[M] \end{cases}$$

which is far from being an isomorphism in general.

The bordism and cobordism theories of a space satisfy the Eilenberg–Steenrod axioms apart from the dimension axiom. This does not mean that the groups $$\Omega^n_G(X)$$ can be effectively computed once one knows the cobordism theory of a point and the homology of the space X, though the Atiyah–Hirzebruch spectral sequence gives a starting point for calculations. The computation is only easy if the particular cobordism theory reduces to a product of ordinary homology theories, in which case the bordism groups are the ordinary homology groups

 * $$\Omega^G_n(X)=\sum_{p+q=n}H_p(X;\Omega^G_q(\text{pt})).$$

This is true for unoriented cobordism. Other cobordism theories do not reduce to ordinary homology in this way, notably framed cobordism, oriented cobordism and complex cobordism. The last-named theory in particular is much used by algebraic topologists as a computational tool (e.g., for the homotopy groups of spheres).

Cobordism theories are represented by Thom spectra MG: given a group G, the Thom spectrum is composed from the Thom spaces MGn of the standard vector bundles over the classifying spaces BGn. Note that even for similar groups, Thom spectra can be very different: MSO and MO are very different, reflecting the difference between oriented and unoriented cobordism.

From the point of view of spectra, unoriented cobordism is a product of Eilenberg–MacLane spectra – MO = H($\pi$∗(MO)) – while oriented cobordism is a product of Eilenberg–MacLane spectra rationally, and at 2, but not at odd primes: the oriented cobordism spectrum MSO is rather more complicated than MO.

Other results
In 1959, C.T.C. Wall proved that two manifolds are cobordant if and only if their Pontrjagin numbers and Stiefel numbers are the same.

title: Cobordism


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Orientation

Orientation may refer to:

Positioning in physical space

 * Map orientation, the relationship between directions on a map and compass directions
 * Orientation (housing), the position of a building with respect to the sun, a concept in building design
 * Orientation of churches, the architectural feature of facing ("orienting"), churches towards the east (Latin: oriens)
 * Coin orientation, a description of the orientation of opposite faces of a coin with respect to one another
 * Page orientation, the way in which a rectangular page is oriented for normal viewing
 * In Animal navigation, turning the body to a desired heading, e.g. in the correct direction of migration
 * Orientation (sign language), the orientation of the hands when signing
 * Terms of orientation, language used to indicate the orientation of objects

Arts and media

 * Orientation (EP), a 2001 album by Sonata Arctica
 * Orientation (film), a 1996 short film produced by the Church of Scientology
 * "Orientation" (Lost), a 2005 episode of American television series Lost
 * "Orientación", an episode of the American television series Prison Break
 * "Orientation" (Heroes), a 2009 episode of American television series Heroes
 * Orientation (Agents of S.H.I.E.L.D.), an episode of the American television series Agents of S.H.I.E.L.D.

Mathematics

 * Orientation (geometry), the direction in which a geometrical object is pointed
 * Orientation (space), the choice, in a space, between "clockwise" and "counterclockwise"
 * Orientation (vector space), the specific case of linear algebra
 * Orientability, a property of a geometrical space which allows choosing an orientation, that is, distinguishing an object in the space from its mirror image
 * Orientation character, a character of the fundamental group that "measures" the orientability of a manifold.
 * Curve orientation, the choice of a direction for a point moving on a curve
 * Orientation (graph theory), an assignment of a direction (orientation) to each edge of an undirected graph

Other uses

 * Orientation (mental), a function of the mind
 * Romantic orientation, the sex or gender with which a person is most likely to have a romantic relationship or fall in love
 * Sexual orientation, the direction of an individual's sexuality with respect to the sex of the persons the individual finds sexually attractive
 * Student orientation, the first week of a university year in several countries

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Orientation


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Michael Chang

Michael Te-pei Chang (born February 22, 1972) is an American former professional tennis player and coach. He is the youngest man in history to win a singles major, winning the 1989 French Open at 17 years and 109 days old. Chang won a total of 34 top-level professional singles titles, (including seven Masters titles) was a three-time major runner-up, and reached a career-best ranking of world No. 2 in 1996. Since he was shorter than virtually all of his opponents, he played a dogged defensive style utilizing his quickness and speed.

In 2008, Chang was inducted into the International Tennis Hall of Fame. He began coaching Kei Nishikori in 2014.

Early life
Michael Te-Pei Chang was born to Joe and Betty Chang on February 22, 1972, in Hoboken, New Jersey. Chang's parents had emigrated to the United States from Taiwan.

After moving from Hoboken to St. Paul, Minnesota, where he learned tennis, Chang and his family moved first to Placentia, California, and then to Encinitas, California, to increase the tennis opportunities for him and his older brother, Carl. Growing up, Chang learned some Chinese from his Taiwanese parents and can speak Mandarin. Betty quit her job as a chemist to travel with Chang on tour. After rising to #163 in the world as a 15-year-old amateur, Chang dropped out of tenth grade at San Dieguito High School in Encinitas to pursue a professional tennis career. He received his GED in February 1988.

Junior career
Chang first came to the tennis world's attention at age 12 as an outstanding junior player who set numerous "youngest-ever" records. Chang first came to the tennis world's attention at age 12 when he won his first national title, the USTA Junior Hard Court singles. At age 13, he won the Fiesta Bowl 16s. In July 1987, at the age of 15, Chang won another USTA Junior Hard Court singles, beating Pete Sampras in the final, and a month later, in Kalamazoo, he won America’s most prestigious junior event, the United States Nationals U18s tournament, beating Jim Courier in the final. This victory earned him a wildcard for the U.S. Open.

Professional career
On 1 September 1987, at age 15, Chang became the youngest player to win a main draw match at the US Open when he defeated Paul McNamee in four sets (6–3, 6–7, 6–4, 6-4) in the first round. A month later, he reached the semifinals at Scottsdale, Arizona, to become the youngest player to reach the semifinal stage of a top-level professional tournament. In 1988, aged 16 years and seven months, he won his first top-level singles title at San Francisco, defeating Johan Kriek in the final. During his title run, Chang registed a 6-4, 6-0 win over Mikael Pernfors, the 1986 French Open finalist who just the previous week had beaten Andre Agassi in the finals of Los Angeles.

Chang's most significant "youngest-ever" record came in 1989 when he won the French Open at the age of 17 years, 114 days, to become the youngest male player ever to win a Grand Slam title. He defeated Stefan Edberg in a five-set final, 6–1, 3–6, 4–6, 6–4, 6–2. Chang thus became the first American man to win the French Open since Tony Trabert in 1955, and the first American man to win a Grand Slam since 1984. His 1989 French Open tournament performance is equally remembered for an epic fourth-round encounter with Ivan Lendl, who was then the world's No. 1-ranked player, was the reigning Australian Open champion, and was a three-time former French Open champion.

In 1988, Chang had been easily beaten by Lendl in an exhibition match held in Des Moines, Iowa. After the match, Lendl advised Chang, "First off, you've got no serve. And you've certainly got no second serve. You can't hurt me. You can run but you better develop a weapon to survive out here", all weaknesses that Chang worked to improve on. At the 1989 French Open, Lendl appeared to be on the way to beating Chang after taking the first two sets 6–4, 6–4 and breaking Chang's serve in his opening service game of the third set. However, Chang broke back immediately and went on to claim the third set, 6–3. During the fourth set, Chang experienced a severe attack of leg cramps, and though he won the set to level the match, he considered retiring from the match while up 2–1 in the fifth set. He later said that he felt "an unbelievable conviction in my heart" not to give up, and decided to finish the match.

Chang adopted some unusual tactics in an attempt to overcome his cramps. Those tactics included hitting shots high into the air (known as "moon balls") to slow the match down and going for more winners in order to shorten the points. The success of these tactics caused Lendl to lose his rhythm and also prompted him to swear at the umpire and the crowd, especially after losing a key point in the fifth set when Chang shocked him by delivering an under-arm serve. On match point, Chang stood just behind the service line while waiting to receive Lendl's second serve. The tactic worked, as Lendl produced a double-fault to give Chang the victory, 4–6, 4–6, 6–3, 6–3, 6–3, in 4 hours and 37 minutes.

Chang subsequently defeated Ronald Agénor in the quarter-final and Andrei Chesnokov in the semi-final. Then seven days after his match against Lendl, after beating Stefan Edberg in five sets, Chang went on to lift the Coupe des Mousquetaires, becoming the youngest men's champion in Grand Slam history. Chang's match against Lendl was played on June 5, 1989, just one day after the height of the Tiananmen Square Massacre. Chang has frequently noted the impact of the massacre when recalling his French Open victory: "A lot of people forget that Tiananmen Square was going on. The crackdown that happened was on the middle Sunday at the French Open, so if I was not practicing or playing a match, I was glued to the television, watching the events unfold...I often tell people I think it was God's purpose for me to be able to win the French Open the way it was won because I was able to put a smile on Chinese people's faces around the world at a time when there wasn't much to smile about."

Chang became the first American man to win the French Open since Tony Trabert in 1955,  and the first American man to win a Grand Slam since 1984. In August 1989, Chang became the youngest player to be ranked in the world's top 5.

Chang would defeat Lendl again in near-duplicate fashion, 2–6, 4–6, 6–4, 7–6 (7–5), 9–7 in a 4-hour, 42-minute semi-final match at the Grand Slam Cup on December 14, 1991.

Chang met Edberg in the semifinals of the US Open in 1992; this time, Edberg won in five sets, 6–7, 7–5, 7–6, 5–7, 6–4. The five-hour, 26-minute match is the longest in US Open history. Chang reached three further Grand Slam finals after his 1989 French Open triumph, losing the 1995 French Open final to Thomas Muster, the 1996 Australian Open final to Boris Becker, and the 1996 US Open final to Pete Sampras. In the 1995 French Open, he defeated Michael Stich and then two-time defending champion Sergi Bruguera in the semifinals in straight sets, eventually losing to Muster. In both the 1996 Australian and U.S. Opens, he defeated Andre Agassi in the semifinals in straight sets; a win over Sampras at the U.S. Open would have made Chang the no. 1 player in the world. In the 1997 U.S. Open, he was the odds-on favorite to win after Sampras was upset by Petr Korda; however, Chang lost to eventual champion Patrick Rafter in the semifinals in straight sets.

Chang is the first player to be beaten by Roger Federer in the main draw of a Grand Slam tournament, at the 2000 Australian Open. He is also the second player to be beaten by Andy Roddick in the main draw of a Grand Slam tournament, in the second round of the French Open in 2001.

Chang was introduced to tennis by his father Joe, who was his first coach. During his rise in 1989 (including his French Open title), he was coached by José Higueras. For much of his professional career, he was coached by his older brother Carl Chang, who also played in several doubles tournaments with him in the early 1990s.

Chang retired from the professional tour in 2003. During his career, he won a total of 34 top-level professional singles titles. His final top-level title was won in 2000 at Los Angeles. His total career prize-money earnings was US$19,145,632. His career-high singles ranking was world no. 2 in 1996, following his US Open finals performance. He was a year-end top-ten player for six consecutive years in the 1990s (1992–1997), a feat matched in the decade only by Pete Sampras. He is one of a few players to win ATP titles in three different decades. His three Indian Wells Masters titles was an ATP record which stood for 15 years, before being eclipsed by Roger Federer in 2012.

Chang's success marked the start of an era in which a new generation of American players—which also included Pete Sampras, Jim Courier, and Andre Agassi—would come to dominate the game.

International play
Chang was a key member of the US team which won the Davis Cup in 1990. In the semifinals in Austria, his dramatic comeback from two-sets down against Horst Skoff, 3–6, 6–7, 6–4, 6–4, 6–3, led the US into its first Davis Cup final since 1984. Chang went on to defeat Darren Cahill in straight sets, as the US defeated Australia in the final. He was also on the US team which won the World Team Cup in 1993. His best performance in the year-end singles championship came in 1995, when he defeated Muster, Jim Courier, and then dominated Pete Sampras in the semifinals, before losing in the final to Boris Becker.

Chang represented the US in the 1992 Summer Olympics in Barcelona, reaching the second round before being eliminated by Jaime Oncins. He chose to skip the 1996 Summer Olympics despite the fact that the event was held in Atlanta and that he would have been the tournament's number-one seed (the singles' gold medal was won by Andre Agassi). Chang participated in the 2000 Summer Olympics in Sydney, where he was eliminated in the first round by Sébastien Lareau.

Awards and recognition

 * Chang won the ATP Newcomer of the Year award in 1988.
 * Chang was awarded ATP Most Improved Player in 1989.
 * In 2008, Chang was inducted into the International Tennis Hall of Fame.
 * On 3 May 2009, Chang was honored by the Los Angeles Chinese Historical Society of Southern California in "Celebrating Taiwanese Americans in Sports".

Equipment and endorsements
Chang signed a multimillion-dollar endorsement deal with Reebok in 1988; he wore Reebok apparel and Reebok Court Victory Pumps shoes during his tennis career and used Prince rackets on court. He started using the Prince "Precision Michael Chang Graphite" 28-inch signature racket in 1994, which was an inch longer than the standard model.

Chang signed endorsement deals with Nissin Foods noodles in 1989, Panasonic and Longines in the 1990s, Cathay Pacific Airlines in 1990, Bristol-Myers Squibb promoting Nuprin in 1991, Stelux watches in 1993, Discover Card in 1996, Tiger Balm, Procter & Gamble (endorsing P&G's Rejoice Shampoo), Eveready Battery Company (endorsing Eveready Alkaline batteries), and Yale locks. In 1997, he signed a multi-year contract to endorse Watch Reebok, a collection of sports watches. A limited edition Michael Chang signature watch was released at Christmas.

Coaching
Chang began coaching Kei Nishikori in 2014.

Business ventures
Chang and his family established CMCB Enterprises, which has real estate holdings including shopping malls, in California, Texas, Arizona and Colorado. In 2003, they bought Dunton Realty Co., a retail brokerage and property management company, and changed its name to Dunton Commercial Real Estate Co. In 2004, they bought SullivanHayes Cos., a retail real estate company in Denver. It was chosen by Denver International Airport to develop a new 17-acre retail project along Peña Boulevard, the airport's main artery.

Charity work
Chang served as Chairman of ATP Tour Charities in 1994. He has supported grassroots tennis development in Asia through his Stars of the Future program in Hong Kong and the Reebok Challenge across Asia. He was one of five athletes named in the second annual "Most Caring Athlete" list by USA Today Weekend in 1995. In 1997, he was given one of seven Asian-American leadership awards by A Magazine for his status as a role model for Asian-American youth. He has also served as a national spokesman for the National Fish and Wildlife Foundation in the US.

In 2001, Chang served as a goodwill ambassador for the 2008 Beijing Olympic bid committee.

Hobbies
Chang is an avid fisherman, and often took fishing trips while traveling for tournaments. In his home in Mercer Island, Washington, he set up several fresh-water aquariums, his largest being 240 gallons, eight-feet long by two feet high, which he uses to breed African cichilds among other things.

Book
In 2002, Chang published a book about his career entitled Holding Serve: Persevering On and Off the Court.

Education
Chang attended the master's in ministry program at Biola University in La Mirada, California, for a year and a half. He serves on Biola's Board of Trustees.

Personal life
On 18 October 2008, Chang married Amber Liu, also a professional tennis player. They have three children, including two daughters. He is a devout Christian.

Singles performance timeline
1 Held as Stockholm Masters until 1994, Stuttgart Masters from 1995 to 2001.

Records

 * Youngest Grand Slam champion, winning French Open, at 17 years, 3 months old (1989).
 * Youngest Grand Slam finalist, playing French Open final, at 17 years, 3 months old (1989).
 * Youngest ever male player to be ranked ATP top-5, at 17 years, 5 months old (1989).
 * Youngest ever male player to be ranked ATP top-5 at the end of the season, at 17 years, 10 months old (1989).
 * Youngest ever male player to be ranked ATP top-10 at the end of the season, at 17 years, 10 months old (1989).

title: Michael Chang


text:
Pamela Jones

Pamela Jones, commonly known as PJ, is the creator and was editor of Groklaw, a website that covered legal news of interest to the free and open-source software community. Jones is an open source advocate who previously trained and worked as a paralegal.

Jones' articles have appeared in Linux Journal, LWN, LinuxWorld Magazine, Linux Today, and LinuxWorld.com. She also wrote a monthly opinion column for the UK print publication Linux User and Developer. She is one of the contributors to the book Open Sources 2.0: The Continuing Evolution.

In 2010 the Electronic Frontier Foundation awarded the Pioneer award to "Pamela Jones and the Groklaw Website" for "Legal Blogging".

Groklaw
Jones had a website, Groklaw, which covered open source legal issues, notably the SCO–Linux disputes. The website started as a blog but grew from there.

Groklaw covered the various lawsuits involving the SCO Group in detail but also covered general legal news of interest to the Free Software and Open Source community. The site won numerous awards, including the Electronic Frontier Foundation Pioneer Award in 2010 and the American Bar Association Journal Blawg 100 in 2012.

Groklaw shut down on August 20, 2013, following the Lavabit email shutdown, because there was "no way to do Groklaw without email", and the inability to privately collaborate without it: "I can't do Groklaw without your input."

Grokline
Jones also launched Grokline, a Unix ownership timeline project, in February 2004.

Grokdoc
Grokdoc was a Groklaw spinoff whose original goal was to create a useful manual on basic Linux tasks that new Linux users will find simple and clear and easy to follow, using what they learn from their study. The site now also supports many other collaborative projects which benefit from its wiki-like structure.

Use of initials
Jones reveals very little personal information, as she considers it private and has expressed from the beginning a strong preference for avoiding fame. Here are the reasons she gave in the early days for using just her initials:

"I originally wanted to stay anonymous, in a sense, by just saying PJ. Eventually media attention and other factors made it impossible to remain just PJ but I would have if I could have. I have no desire to be famous, for one thing.  And  I have been creatively influenced by Scott McCloud's work.  He points out in Understanding Comics  (p. 45–51) in a section on iconic representation that people respond most strongly to a drawing of a character that simplifies to the point that anyone can identify with the character.  I guess I was hoping for that effect.  In other words, I was hoping people could assume whatever they wanted and just focus on what I said, rather than on who was saying it. For that reason, I chose PJ, because it could be anyone, either sex, any nationality, anyone and no one in particular.  I wanted participation by anyone interested in the SCO story. No politics.  Nothing extraneous. Just an effort to locate and provide evidence that could be useful. I knew the community could answer SCO, if they just knew what was needed. And they have."

Publications

 * Articles in Linux Journal, Linux World, Linux Today, LWN.
 * Monthly column in LinuxUser, a UK print publication.
 * Contributor to Open Sources 2.0: The Continuing Evolution.
 * This article has been highly influential in articulating thought on free licenses.

title: Pamela Jones


text:
St Ethelburga's Bishopsgate

St Ethelburga-the-Virgin within Bishopsgate is a Church of England church in the City of London, located on Bishopsgate near Liverpool Street station.

One of the few surviving medieval City churches in London, the foundation date of the church is unknown, but it was first recorded in 1250 as the church of St Adelburga the Virgin.

The church was rebuilt around 1411 and some of this material remains, notably in the south arcade.

The church was severely damaged by an IRA bomb in 1993. Following rebuilding and restoration it re-opened as a Centre for Reconciliation and Peace.

History
This structure is a rare survivor of the medieval City churches that were mostly destroyed during the Great Fire of London in 1666. It is dedicated to St Ethelburga, a 7th-century abbess of Barking Abbey; she was the sister of Saint Erkenwald, a Bishop of London. Its foundation date is unknown, but it was first recorded in 1250 as the church of St Adelburga-the-Virgin. The dedication to "-the-Virgin" was dropped in Puritan times but was later restored. The church was rebuilt in the 15th century – possibly around 1411 – and a small square bell turret was added in 1775. A weathervane was added in 1671. In order to raise revenue for the church, whose parish covered just three acres (1.2 ha), a wooden porch was built over its exterior in the 16th century to house two shops. It underwent major changes in 1932, when Bishopsgate was controversially widened. The shops were demolished and the porch dismantled, revealing the façade of the church for the first time in centuries.

It suffered modest bomb damage during the Blitz of the Second World War and was restored in 1953. In 1993, the church was half destroyed when a massive IRA bomb exploded 7 metres from the church, devastating Bishopsgate and causing an estimated £350 million worth of damage. An evangelical faction of the Church of England proposed to demolish St Ethelburga's in the aftermath but, following a sustained public outcry, it was rebuilt to its original plan, though much changed inside.

Description
The church's tiny interior comprises a nave and aisle divided by an arcade. Most of the original fittings were destroyed by the 1993 bombing although they were not as old as the church. Dating from the early 20th century, they were the work of Ninian Comper. One of the more notable surviving elements is the curious 19th-century font, which is inscribed with one of the longest known palindromes, written in Greek: ΝΙΨΟΝ ΑΝΟΜΗΜΑΤΑ ΜΗ ΜΟΝΑΝ ΟΨΙΝ, which translates as "Cleanse [your] transgressions, not only [your] face".

The church was designated a Grade I listed building on 4 January 1950, and its reconstruction retains the listing.

Centre for Reconciliation and Peace
St Ethelburga's Centre for Reconciliation and Peace is a non-profit charity which aims to build relationships across divisions of conflict, culture and religion. Its work includes: a multi-faith conflict resilience programme (faith leaders working together to become more intelligent in their responses to conflict); community reconciliation (building a coalition for peace within the North and South Sudanese diaspora in London); the Narrative Practitioners Forum (promoting the use of narrative and personal story for building empathy between people with different backgrounds); Re-awakening the Sacred (a secular and spiritual multi-disciplinary enquiry into bringing a deeper sense of meaning into the earth, environment, leadership, economics and business etc.); an MA in reconciliation at Winchester University; and several strands of cultural exchange work mentoring young adults into social action leadership roles.

It also runs a certificated three-day course in conflict coaching aimed at anyone dealing with workplace or personal conflict.

The centre also works with a social enterprise, Seasoned Events, for building/venue hire purposes.

Every year the Centre organises a 10km walk, 'The Ethelburga Walk', which links two historic sites associated with the St Ethelburga of Barking: Barking Abbey and St Ethelburga's Centre.

St Ethelburga's is a partner in the community of the Cross of Nails.

Notable people associated with the church

 * Blessed John Larke, Rector (1504–1544) who was martyred for denying the royal supremacy in matters spiritual.
 * Henry Hudson, explorer, took communion with his crew before setting out in search of the Northwest Passage, 1607.
 * Charles Viner (1678-1756) married in the church in 1699.
 * John Medows Rodwell, Rector (1843–1900) who made the first reliable rendering of the Qur'an into English (1861).
 * W. F. Geikie-Cobb, Rector (1900–1941) who achieved notoriety by marrying many divorced persons in the church.
 * Singers Webster Booth and Anne Ziegler (born Irené Frances Eastwood) had their marriage blessed by W. F. Geikie-Cobb in a special ceremony for divorced persons on 5 November 1938.

title: St Ethelburga's Bishopsgate


text:
Cathare

Cathare is a goat's milk cheese from the Languedoc-Roussillon region of France. The cheese comes in flat discs whose face is covered in charcoal powder with the Occitan cross inscribed. Under the rind, Cathare is pure white with a soft, creamy texture. Its goat-milk flavor intensifies as it ages, and reaches its prime after two to three weeks, which makes it typically unavailable in the United States, due to the Food and Drug Administration's stance that raw milk soft cheeses can pose a health risk. The sale of raw milk cheese aged under 60 days is illegal in the United States.

title: Cathare


text:
Talk:Cambridge Conference Network

Orphan
This is an orphan. could someone familiar with the topic link this article to another? Kingturtle 11:17, 7 Dec 2003 (UTC)
 * I believe this is the same system used by the University of Toronto (their system is called CCNet, but it's used for course websites, not for information accessibility); is there any way that article could link here?

Cleanup
I have given the article a bit of a rewrite and added details of the organisation's views on climate change in particular. I am concerned that the only references are back to the organisation's own website, hence the use of the word 'claim' in relation to its membership. I also an concerned that the last post was made over 3 years ago. PeterEastern (talk) 15:17, 26 September 2009 (UTC)

Various issues
I edited some refs as follows:
 * Reduced redundancy (there were two refs to the same Times Higher Education article).
 * Noted that the CCNet homepage link is a dead link.
 * Removed 'The Colbert Report' as per WP:CIRCULAR.
 * Noted failed verifications (in relation to hate mail from children).

Additional issue:
 * Article title is "CCNet (network)" which gives the impression of being a physical network (such as a computer network). For accuracy, perhaps "(network)" should be changed to something like "(online discussion forum)", "(online chat room)", "(online publication)", etc.  This is also to prevent it from being confused with CCNET which was an actual computer network (as noted on the DECnet page).  I propose to update the title accordingly.

If there is any alternate proposal, please discuss here. Thanks. -- HLachman (talk) 22:10, 12 July 2014 (UTC)

 * Agree that it should be changed. It should also be removed from the category "Academic computer network organizations" since this seems to consist of physical computer network providers for academic institutions in various countries. It was never a chat room, nor really a publication. As far as I can tell from receiving CCNET emails for a few years (and from the archive of posts) is that it was just an email list. Hence "CCNet (email list)" might be better? An alternative is to delete the page if it isn't notable. Is an email list ever notable? The email list and hence CCNET are no longer active and the archive page has been removed (though there is a copy of posts up to July 2006 on the wayback machine ). TimOsborn (talk) 07:47, 14 July 2014 (UTC)

 * I made some layout edits, grouping sentences into paragraphs and a section on climate change. Also removed the Academic computer network organizations category, as noted above. Despite making these edits, I can't see why CCNet is notable. TimOsborn (talk) 10:20, 14 July 2014 (UTC)

Thanks, TimOsborn. In light of your responses, and the lack of any dissenting comments (over the past month), I went ahead with my proposal (above) and moved the article (renamed it from "CCNet (network)" to "Cambridge Conference Network") and made corresponding adjustments in the article.

Also in light of TimOsborn's comments (e.g., "Is an email list ever notable?"), and the fact that this subject matter is covered in Benny Peiser, I further propose a merger of this article with the latter article. The target article seems to already contain all the essential information from this article, and more. So this might not require any editing, just that this article name becomes a redirect to the relevant section of the aforementioned (Benny Peiser) article, and this article ceases to exist (except as a redirect). If there are any opinions, please discuss here. Thanks. -- HLachman (talk) 04:43, 18 August 2014 (UTC)

 * I support HLachman's proposal for a merger. As far as I have seen, CCNet is intrinsically linked with Benny Peiser (e.g. none of the archived archives I looked at were edited by anyone but Peiser) so it fits best on Peiser's page as one of his notable activities. TimOsborn (talk) 23:35, 20 August 2014 (UTC)

Thanks for your comments. In light of the above merger discussion, I am doing a blank-and-redirect (WP:BLAR), so that this article (Cambridge Conference Network) will now redirect to the above-mentioned Benny Peiser article. I will add further comments at Talk:Benny Peiser. Please post any further discussion there. -- HLachman (talk) 10:51, 21 September 2014 (UTC)

title: Talk:Cambridge Conference Network


text:
List of towns in New Zealand

This is a list of towns in New Zealand. The term "town" has no current statutory meaning in New Zealand, the few "Town Districts" having been abolished in 1989 or earlier.

The list includes most urban areas in New Zealand. Those deemed urban areas by Statistics New Zealand (under either the NZSCA92 or SSGA18 standard) are marked with an asterisk. Isolated towns, such as Ashburton and Levin, are usually parts of a local government "District" (which occasionally has the same name), but the rest, such as Wainuiomata, Pukerua Bay, and Port Chalmers, are within city council boundaries, and are often referred to as suburbs of their respective cities. Many were boroughs during most of the twentieth century, and some earlier.

A

 * Ahaura
 * Ahipara
 * Ahititi
 * Ahuroa
 * Aka Aka
 * Akaroa
 * Ākitio
 * Albert Town
 * Albury
 * Alexandra*
 * Allanton
 * Amberley*
 * Anakiwa
 * Arahiwi
 * Aramoana
 * Aranga
 * Arapohue
 * Arrowtown*
 * Arundel
 * Ashburton*
 * Ashhurst*
 * Ashley
 * Ātiamuri
 * Auckland*
 * Auroa
 * Awanui

B

 * Baddeleys Beach
 * Balclutha*
 * Balfour
 * Barrhill
 * Barrytown
 * Beachlands*
 * Beaumont
 * Bell Block
 * Benhar
 * Benneydale
 * Bideford
 * Blackball
 * Blenheim*
 * Bluff*
 * Brighton*
 * Brightwater*
 * Broadwood
 * Bulls*
 * Bunnythorpe
 * Burnt Hill

C

 * Cambridge*
 * Campbells Beach
 * Canvastown
 * Carterton*
 * Charlton
 * Chatton
 * Cheviot
 * Christchurch*
 * Clarksville
 * Clarkville
 * Clevedon
 * Clinton
 * Clive*
 * Clyde
 * Coatesville
 * Collingwood
 * Colville
 * Cooks Beach
 * Coopers Creek
 * Coroglen
 * Coromandel*
 * Cromwell*
 * Culverden
 * Cust

D

 * Dairy Flat
 * Dannevirke*
 * Darfield*
 * Dargaville*
 * Dipton
 * Dobson
 * Dome Valley
 * Doyleston
 * Drury
 * Dunedin*
 * Duntroon

E

 * Eastbourne
 * Edendale
 * Edgecumbe*
 * Egmont Village
 * Eketāhuna
 * Eltham*
 * Ettrick
 * Eyrewell Forest

F

 * Fairhall
 * Fairlie
 * Fairfax
 * Fairview
 * Featherston*
 * Feilding*
 * Fencourt
 * Fernside
 * Flaxmere
 * Flaxton
 * Fox Glacier
 * Foxton*
 * Foxton Beach*
 * Frankton
 * Franz Josef / Waiau

G

 * Geraldine*
 * Gisborne*
 * Glen Massey
 * Glenorchy
 * Glentui
 * Glorit
 * Gordonton
 * Gore*
 * Granity
 * Greymouth*
 * Greytown*
 * Grovetown
 * Gummies Bush

H

 * Haast
 * Hakataramea
 * Halcombe
 * Hamilton*
 * Hampden
 * Hanmer Springs
 * Hari Hari
 * Harrisville
 * Haruru
 * Hastings*
 * Haumoana
 * Haupiri
 * Havelock
 * Havelock North*
 * Hāwera*
 * Helensville*
 * Henley
 * Herbert
 * Herekino
 * Hikuai
 * Hikurangi*
 * Hikutaia
 * Hinuera
 * Hokitika*
 * Honikiwi
 * Hope*
 * Horeke
 * Horotiu
 * Horsham Downs
 * Houhora
 * Huapai*
 * Huiakama
 * Huirangi
 * Hūkerenui
 * Hunterville
 * Huntly*
 * Hūnua
 * Hurleyville

I

 * Inangahua Junction
 * Inglewood*
 * Invercargill*
 * Irwell

J

 * Jack's Point
 * Jacobs River

K

 * Kaeo
 * Kaiapoi*
 * Kaihu
 * Kaikohe*
 * Kaikōura*
 * Kaimata
 * Kaingaroa, Northland
 * Kaingaroa, Bay of Plenty
 * Kaipara Flats
 * Kairaki
 * Kaitaia*
 * Kaitangata
 * Kaiwaka
 * Kakanui
 * Kakaramea
 * Kaniere
 * Kapiro
 * Kaponga
 * Karamea
 * Karetu
 * Karitane
 * Katikati*
 * Kauaeranga
 * Kaukapakapa
 * Kauri
 * Kawakawa*
 * Kawerau*
 * Kekerengu
 * Kennedy Bay
 * Kerikeri*
 * Kihikihi
 * Kingston
 * Kinloch
 * Kiripaka
 * Kirwee
 * Kohukohu
 * Koitiata
 * Kokatahi
 * Kokopu
 * Koromiko
 * Kumara
 * Kumeū*
 * Kurow

L

 * Lake Hāwea
 * Lake Tekapo
 * Langs Beach
 * Lauriston
 * Lawrence
 * Leeston*
 * Leigh
 * Lepperton
 * Levin*
 * Lincoln*
 * Linkwater
 * Little River
 * Loburn
 * Lower Hutt*
 * Luggate
 * Lumsden
 * Lyttelton*

M

 * Mahurangi West
 * Makahu
 * Mamaku
 * Manaia, Waikato
 * Manaia, Taranaki
 * Manakau
 * Manapouri
 * Manawahe
 * Mangakino
 * Mangamuka
 * Mangatangi
 * Mangatāwhiri
 * Mangatoki
 * Mangawhai*
 * Manukau
 * Manurewa
 * Manutahi
 * Māpua*
 * Maraetai*
 * Mārahau
 * Marco
 * Maromaku
 * Marsden Bay*
 * Martinborough*
 * Marton*
 * Maruia
 * Masterton*
 * Matakana
 * Matakohe
 * Matamata*
 * Matapu
 * Matarangi
 * Matarau
 * Matatā
 * Mataura*
 * Matihetihe
 * Maungakaramea
 * Maungatapere
 * Maungaturoto
 * Mayfield
 * Medlands Beach
 * Meremere
 * Methven*
 * Middlemarch
 * Midhirst
 * Millers Flat
 * Milton*
 * Mimi
 * Minginui
 * Moana
 * Moawhango
 * Moenui
 * Moeraki
 * Moerewa*
 * Mōkau
 * Mokoia
 * Morrinsville*
 * Mosgiel*
 * Mossburn
 * Motatau
 * Motueka*
 * Motuoapa
 * Mount Maunganui
 * Mount Somers
 * Murchison
 * Murupara*

N

 * Napier*
 * Naseby
 * National Park
 * Nelson*
 * New Brighton
 * New Plymouth*
 * Ngaere
 * Ngākuta Bay
 * Ngamatapouri
 * Ngapara
 * Ngāruawāhia*
 * Ngataki
 * Ngatea*
 * Ngawi
 * Ngongotahā*
 * Ngongotahā Valley
 * Ngunguru*
 * Nightcaps
 * Norfolk
 * Normanby
 * Norsewood

O

 * Ōakura*
 * Oamaru*
 * Oban
 * Ōhaeawai
 * Ohakune*
 * Ohangai
 * Ōhaupō
 * Ohawe
 * Ohoka
 * Ōhope*
 * Ōhura
 * Ōkaihau
 * Ōkato
 * Ōkiwi Bay
 * Okuku
 * Ōmaha
 * Omanaia
 * Omarama
 * Omata
 * Ōmokoroa*
 * Onewhero
 * Opononi
 * Ōpōtiki*
 * Opua*
 * Ōpunake*
 * Oratia
 * Orewa
 * Oromahoe
 * Oruaiti
 * Otaika
 * Ōtaki*
 * Otakou
 * Ōtaua in Northland
 * Otaua in Waikato
 * Otautau
 * Otematata
 * Otiria
 * Ōtorohanga*
 * Ōwhango
 * Owaka
 * Oxford*

P

 * Paekākāriki*
 * Paeroa*
 * Pahiatua*
 * Paihia*
 * Pakaraka
 * Pākiri
 * Pakotai
 * Palmerston
 * Palmerston North*
 * Pamapuria
 * Panguru
 * Papamoa
 * Paparoa
 * Paparore
 * Papatoetoe
 * Parakai
 * Paraparaumu*
 * Pāremoremo
 * Pareora
 * Parewanui
 * Paroa
 * Parua Bay
 * Patea*
 * Patumāhoe*
 * Pauanui
 * Pāuatahanui
 * Pegasus*
 * Peka Peka
 * Pembroke
 * Peria
 * Petone
 * Picton*
 * Piopio
 * Pipiwai
 * Pirinoa
 * Pirongia
 * Pleasant Point*
 * Plimmerton
 * Plummers Point
 * Point Wells
 * Pōkeno
 * Porirua*
 * Poroti
 * Port Chalmers
 * Portland
 * Portobello
 * Puhoi
 * Pukekohe*
 * Pukehina
 * Pukepoto
 * Pukerimu
 * Pukerua Bay
 * Puketona
 * Pukeuri
 * Punakaiki
 * Purua
 * Putāruru*
 * Putorino

Q

 * Queenstown*

R

 * Raetihi*
 * Raglan*
 * Rahotu
 * Rai Valley
 * Rainbows End
 * Rakaia*
 * Ramarama
 * Ranfurly
 * Rangiora*
 * Rapaura
 * Rārangi
 * Ratapiko
 * Raumati Beach
 * Raumati South
 * Raurimu
 * Rawene
 * Rawhitiroa
 * Reefton*
 * Renwick*
 * Reporoa
 * Richmond*
 * Riverhead*
 * Riverlands
 * Riversdale
 * Riversdale Beach
 * Riverton / Aparima*
 * Riwaka
 * Rolleston*
 * Ross
 * Rotorua*
 * Roxburgh
 * Ruakākā
 * Ruatoria
 * Ruawai
 * Runanga*
 * Russell

S

 * Saint Andrews
 * Saint Arnaud
 * Saint Bathans
 * Sanson
 * Seacliff
 * Seddon
 * Seddonville
 * Sefton
 * Shannon*
 * Sheffield
 * Shelly Beach
 * Silverdale
 * Snells Beach*
 * Spring Creek
 * Springfield
 * Springs Junction
 * Springston
 * Stirling
 * Stratford*
 * Swannanoa

T

 * Taharoa
 * Taieri Mouth
 * Taihape*
 * Taipa-Mangonui*
 * Tairua*
 * Tākaka*
 * Tangiteroria
 * Tangowahine
 * Tapanui
 * Tapawera
 * Tāpora
 * Tapu
 * Taradale
 * Tauhoa
 * Taumarunui*
 * Taupaki
 * Taupō*
 * Tauranga*
 * Tauraroa
 * Tautoro
 * Te Anau*
 * Te Ārai
 * Te Aroha*
 * Te Awamutu*
 * Te Awanga
 * Te Hana
 * Te Hāpua
 * Te Horo
 * Te Kao
 * Te Kauwhata*
 * Te Kōpuru
 * Te Kūiti*
 * Te Poi
 * Te Puke*
 * Te Puna West
 * Te Puru
 * Te Rahu
 * Te Rerenga
 * Temuka*
 * Thames*
 * Thornton Bay
 * Ti Point
 * Tikorangi
 * Timaru*
 * Tinopai
 * Tinwald
 * Tīrau
 * Titoki
 * Tokanui, Southland
 * Tokanui, Waikato
 * Tokarahi
 * Toko
 * Tokomaru
 * Tokoroa*
 * Tolaga Bay
 * Tomarata
 * Towai
 * Tryphena
 * Tuahiwi
 * Tuai
 * Tuakau*
 * Tuamarina
 * Tuatapere
 * Tūrangi*
 * Turua
 * Twizel*

U

 * Umawera
 * Upper Hutt*
 * Upper Moutere
 * Urenui
 * Uruti

W

 * Waddington
 * Waharoa
 * Waiau
 * Waiau Pa
 * Waiharara
 * Waiheke Island*
 * Waihi*
 * Waihi Beach*
 * Waihola
 * Waikaia
 * Waikaka
 * Waikanae*
 * Waikawa, Marlborough
 * Waikawa, Southland
 * Waikouaiti*
 * Waikuku
 * Waikuku Beach
 * Waimā
 * Waimangaroa
 * Waimate*
 * Waimate North
 * Waimauku
 * Wainui
 * Wainuiomata
 * Waiomu
 * Waioneke
 * Waiotira
 * Waiouru*
 * Waipango
 * Waipawa*
 * Waipu*
 * Waipu Cove
 * Waipukurau*
 * Wairakei
 * Wairau Valley
 * Wairio
 * Wairoa*
 * Waitahuna
 * Waitara*
 * Waitaria Bay
 * Waitati
 * Waitoa
 * Waitoki
 * Waitomo
 * Waitoriki
 * Waitōtara
 * Waiuku*
 * Waiwera
 * Wakefield*
 * Wallacetown
 * Walton
 * Wānaka*
 * Ward
 * Wardville
 * Warkworth*
 * Warrington
 * Waverley
 * Wellington*
 * Wellsford*
 * Weston
 * Westport*
 * Whakamaru
 * Whakatāne*
 * Whananaki
 * Whangamatā*
 * Whangamōmona
 * Whanganui*
 * Whangaparāoa*
 * Whangārei*
 * Whangārei Heads
 * Whangaruru
 * Whangateau
 * Whataroa
 * Whatuwhiwhi
 * Whenuakite
 * Whenuakura
 * Whiritoa
 * Whitby
 * Whitford
 * Whitianga*
 * Willowby
 * Wimbledon
 * Winchester
 * Windsor, Invercargill
 * Windsor, North Otago
 * Windwhistle
 * Winscombe
 * Winton*
 * Woodbourne
 * Woodend*
 * Woodend Beach
 * Woodhill
 * Woodville*
 * Wyndham

title: List of towns in New Zealand


text:
Talk:Jacqueline Kennedy Onassis

Jackie and Declan Costello
The following is an extract from the newly updated Declan Costello article

Do other editors feel a short synopsis of the above warrants inclusion in the College and early career subsection of Jackie's article, or would it be considered too trivial given the scope of her life? I'm not sure how many or how few credible suitors Jackie had before her first marriage. For reference, the "Costello" family mentioned above is the family of John A. Costello, who at the time was Taoiseach (Prime Minister) of Ireland. That is to say, the most politically powerful man in Ireland at the time. Also, while the above doesn't get into it, Jackie continued to correspond sporadically with both Father Joseph Leonard and Costello as late as the late 1960s, if that influences how people view whether this was trivial or significant relantionship. CeltBrowne (talk) 01:03, 10 January 2022 (UTC)

 * It's a mildly interesting sidelight in the lives of Jackie and Declan, but I'm not sure it even belongs in the Declan article. The quotations by Jackie are the only thing that rise above the background, but they don't really seem to justify inclusion of the anecdote in this article, since there never was an actual dating relationship between the two principals. DonFB (talk) 08:02, 10 January 2022 (UTC)

Semi-protected edit request on 17 January 2022
Under the section RELATIONSHIP TO ROBERT F KENNEDY

"He credited *Kennedy* with convincing him to stay in politics..."

The reference to Kennedy can be confusing since there's several Kennedy's mentioned in the article.

I suggest changing it to...

"He credited *Jacqueline* with convincing him to stay in politics..." 50.5.111.73 (talk) 07:17, 17 January 2022 (UTC)

 * Clarified that section, thanks for spotting. --Marbe166 (talk) 07:37, 17 January 2022 (UTC)

 * Just to clarify: the subject of the article is always the only one who is referred to using a bare surname. Others are referred to by their first names (if related) or their full names (if unrelated). Exceptions are for lists of family members or when the usage of surname alone would be confusing in the context. All other Kennedys here should be referred to by their first names only. MOS:SAMESURNAME WP Ludicer (talk) 23:32, 26 July 2023 (UTC)

Style of surname in article
Much of the article refers to her with the surname "Kennedy" rather than "Kennedy Onasis". The article should either have its title changed, or the body of the article should probably be corrected to refer to her as "Kennedy Onasis". SecretName101 (talk) 00:02, 23 October 2022 (UTC)
 * No. The body of the article refers to her in different places by the name she used at the time being discussed.  This has come up during the years of editing this piece and this is the method that is most sensible and comprehensible.  It's  not a typical situation, so we adapt the usual rules to make the most sense.  Not changing the title of the article either  - this has been the stable name for almost 20 years and it is the name she used for the majority of her life. Tvoz / talk 04:26, 23 October 2022 (UTC)
 * The name she used and her common name can indeed differ. The question is what name she most commonly was referred to by the public.
 * There are areas of the article that need to be double-checked for what name they use. There are many areas that are interchanging the name usage in confusing ways. SecretName101 (talk) 06:28, 23 October 2022 (UTC)
 * And, that fact that the article has used this name for a long name is not an argument against re-assessing the name. Plenty of articles have changed long-standing names. The article "Impeachment and acquittal of Andrew Johnson" was renamed to Impeachment of Andrew Johnson after nearly a decade. The article for Kyiv was long spelled "Kiev" (likely since near the creation of this project) until being renamed within this last year or so.
 * You can re-assess things. SecretName101 (talk) 06:32, 23 October 2022 (UTC)
 * I agree that the article should refer to her in different places by the name she used at the time being covered. In legacy text, she should be called "Onassis" only (like it or not). --SergeWoodzing (talk) 12:04, 1 August 2023 (UTC)

Summary might be too long
Yourlocallordandsavior (talk) 02:47, 1 August 2023 (UTC)

Infobox Image Proposal
Hello, there. I have reason to believe that this image is in the public domain and is a suitable replacement for the current one. Less light is concentrated on her face, not as blurry, et cetera.

That's all. Thanks. 71.184.82.123 (talk) 02:10, 2 May 2024 (UTC)

title: Talk:Jacqueline Kennedy Onassis


text:
Bushy Park

Bushy Park in the London Borough of Richmond upon Thames is the second largest of London's Royal Parks, at 445 ha in area, after Richmond Park. The park, most of which is open to the public, is immediately north of Hampton Court Palace and Hampton Court Park and is a few minutes' walk from the west side of Kingston Bridge. It is surrounded by Teddington, Hampton, Hampton Hill and Hampton Wick and is mainly within the post towns of Hampton and Teddington, those of East Molesey and Kingston upon Thames taking the remainder.

In September 2014, most of it was designated a biological Site of Special Scientific Interest together with Hampton Court Park and Hampton Court Golf Course as Bushy Park and Home Park SSSI. The park is listed at Grade I on the Register of Historic Parks and Gardens.

History
The area now known as Bushy Park has been settled for at least the past 4,000 years: the earliest archaeological records that have been found on the site date back to the Bronze Age. There is also evidence that the area was used in the medieval period for agricultural purposes.

When Henry VIII took over Hampton Court Palace from Cardinal Thomas Wolsey in 1529, the King named three parks that make up modern-day Bushy Park and a small area beside: Hare Warren, Middle Park and Bushy Park. A keen hunter, he established them as deer-hunting grounds.

His successors, perhaps less involved in traditional sporting activities, added a number of picturesque features, including the Longford River, a 19 km canal built on the orders of Charles I to provide water to Hampton Court, and the park's various ponds. This period also saw the construction of the main thoroughfare, Chestnut Avenue, which runs from Park Road in Teddington to the Lion Gate entrance to Hampton Court Palace in Hampton Court Road. This avenue and the Arethusa 'Diana' Fountain were designed by Sir Christopher Wren as a grand approach to Hampton Court Palace.

The park has long been popular with locals, but also attracts visitors from further afield. From the mid-19th century until World War II, Londoners came here to celebrate Chestnut Sunday and to see the abundant blossoming of the trees along Chestnut Avenue. The customs were discovered and resurrected in 1993 by Colin and Mu Pain.

Among those who served as ranger (an honorary position, long including residence at Bushy House) was King William IV, while Duke of Clarence (1797–1830). To ensure his consort Queen Adelaide, could remain at their long-time home after his death, he immediately appointed her as his successor as ranger (1830–1849), after whose death the position was left vacant and fell into disuse.

During World War I, Bushy Park housed the King's Canadian Hospital in the modern "White Lodge", and between the wars it hosted a camp for undernourished children.

During World War II, General Dwight D. Eisenhower planned the D-Day landings from Supreme Headquarters Allied Expeditionary Force (SHAEF) at Camp Griffiss in the Park. A memorial by Carlos Rey dedicated to the Allied troops who fell on D-Day now marks the spot where General Eisenhower's tent stood. The nearby Eisenhower House is named in the General's honour, and Shaef Gate is named after the Supreme Headquarters Allied Expeditionary Force.

From May 1942, a group of temporary buildings on the north-east of the park, codenamed Widewing, hosted the de facto headquarters of the US Eighth Air Force under Generals Carl Spaatz and, later, Ira Eaker. Spaatz went on to command the US Army Air Forces throughout the European Theatre of Operations (ETO) and in early 1944 became commander of the newly formed US Strategic Air Forces (USSTAF) in Europe at Widewing. Also known by its US Army code, AAF-586, Camp Griffiss/Widewing was often confused with the wartime headquarters of VIII Fighter Command (part of Eighth Air Force) at Bushey Hall, near Watford, Hertfordshire. The park also had a runway for planes.

The park today
Originally created for royal sports, Bushy Park is now home to Teddington Rugby Club and four cricket clubs – Teddington Town Cricket Club, Hampton Wick Royal Cricket Club, Teddington Cricket Club, and Hampton Hill Cricket Club. Teddington Hockey Club was based in the Park until it moved to Teddington School; from 1871 onwards, the rules of the modern game of field hockey were largely devised at Bushy. It also has fishing and model boating ponds, horse rides, formal plantations of trees and other plants, wildlife conservation areas, and herds of both red deer and fallow deer.

The park also contains several lodges and cottages: Bushy House, housing the National Physical Laboratory (NPL) at the Teddington end, and the Royal Paddocks and two areas of allotments – the Royal Paddocks Allotments at Hampton Wick and the Bushy Park Allotments at Hampton Hill.

The original Parkrun began in Bushy Park in October 2004, initially as the 'Bushy Park Time Trial', then Bushy Parkrun. It is a free, timed, 5K run that takes place every Saturday morning at 9am, attracting up to 1,500 runners each week. Events also take place annually on Christmas Day and New Year's Day.

As part of an upgrade of the park facilities, the new Pheasantry Café was added, and the restored and largely reconstructed Upper Lodge Water Gardens were opened in October 2009. The work was supported by the Heritage Lottery Fund.

Flora and fauna
Bushy Park is part of the Bushy Park and Home Park SSSI designated in September 2014 for its range of semi-natural habitats such as acid and neutral grassland, scrubland, woodland, and wood pasture. There is an internationally important assemblage of invertebrates due to the mosaic of habitats including two hundred veteran trees. A fungus gnat – a type of fly – new to the UK was found in the Waterhouse Woodland Gardens by entomologist Peter Chandler and identified as Grzegorzekia bushyae and also known as the Bushy Gnat. This fly has since been found in a forest in south-east France.

Transport
The closest railway stations are Hampton Court in East Molesey to the south, Hampton Wick to the east, Teddington and Fulwell to the north, and Hampton to the west. All are within a 10- to 20-minute walk.

Transport for London bus routes 111, 216, and 411 pass the Hampton Court Gate on Hampton Court Road (the main southern entrance to the Park).

R70, R68, and 285 buses stop near the two Hampton Hill Gates off the High Street, while the R68 also serves the Blandford Road Gate (next to the NPL on Hampton Road, Teddington) before continuing to Hampton Court Green via Hampton Hill.

To the north, the main Teddington gate on Park Road, and a second on Sandy Lane, are only served by a half-hourly 481 bus service. But, the main gate is best reached, either on foot or by bike, from Teddington's town centre, which is served by the 33, 281, 285, 481, R68, and X26 services, via Park Road, or from the railway station.

The main north and south gates, connected by the Chestnut Avenue private highway, provide vehicle access to traffic from 6.30am until dusk (or to 7.00pm in the winter months). There is one straight road through the Park between the two gates but cars are no longer permitted to drive straight through the Park, and can only access respective car parks from either gate.

There is 24/7 bicycle access via the main avenue between the north and south gates and cycle paths/restricted access private highways across the park.

title: Bushy Park


text:
Vera-Ellen

Vera-Ellen (born Vera-Ellen Rohe; February 16, 1921 – August 30, 1981) was an American dancer and actress. She is remembered for her solo performances as well as her work with partners Fred Astaire, Gene Kelly, Danny Kaye, and Donald O'Connor. She is best known for her starring roles in On the Town (1949) with Gene Kelly and White Christmas (1954) with Danny Kaye.

Early life
Vera-Ellen Rohe was born in Norwood, Ohio, to Martin F. Rohe, a piano dealer, and Alma C. Westmeier. Both were descended from German immigrants. Her mother dreamed she would have a girl named Vera-Ellen, including the hyphen.

She began dancing at age 10 and quickly became proficient. One of her fellow dance students at Hessler Studio of Dancing was Doris Day. At age 13, she was a winner on the Major Bowes Amateur Hour and embarked upon a professional career.

Stage
In 1939, she made her Broadway debut in the Jerome Kern/Oscar Hammerstein musical Very Warm for May. She became one of the youngest Rockettes at Radio City Music Hall. This led to roles on Broadway in Panama Hattie, By Jupiter, and A Connecticut Yankee, where she was spotted by Samuel Goldwyn, who cast her opposite Danny Kaye and Virginia Mayo in the 1945 film Wonder Man.

Dubbing
Starting in 1945 with Wonder Man, her first film, her singing was dubbed. However, the Decca Broadway Original Cast Album of 1943's revival of A Connecticut Yankee has two vocals by Vera-Ellen, "I Feel at Home with You" and "You Always Love the Same Girl," both duets with Chester Stratton. Her style is of a comic soubrette.

Film
She danced with Gene Kelly in the Hollywood musicals Words and Music and On the Town, while also appearing in the last Marx Brothers film, Love Happy. She received top billing alongside Fred Astaire in the musicals Three Little Words and The Belle of New York. She had a co-starring role with Donald O'Connor in the Ethel Merman vehicle Call Me Madam. She also starred in the 1951 musical comedy Happy Go Lovely alongside David Niven and Cesar Romero. Vera-Ellen's penultimate film role was the 1954 blockbuster hit White Christmas, co-starring with Bing Crosby, Danny Kaye, and Rosemary Clooney. She starred in only one more film, the 1957 British production Let's Be Happy.

Television
Vera-Ellen was a frequent guest on US variety programming in the mid-to-late 1950s. Her final performances were on a November 22, 1958, television episode of The Perry Como Show and a February 14, 1959, broadcast of The Dinah Shore Show. Following that, Vera-Ellen retired from performing.

Personal life
According to Hollywood chronicler Brian Cronin, what he describes as Vera-Ellen's "extremely thin" appearance led to rumors during her career that she had an eating disorder. A rumor that her neck was always covered during the filming of White Christmas because of wrinkling caused by supposed anorexia persists to this day. However, pictures and video taken at the same time show her neck appearing normal and undamaged. A friend, Bill Dennington, who knew her during the last 20 years of her life, dismissed the story about her neck and added that he hated "that people think of her as 'the dancer with anorexia' and not just the fabulous dancer who has been so overlooked."

Her niece by marriage, Ileana Rothschild, born in 1967, remembered that her aunt "never stopped taking dance classes and maintained her slim figure always." She was also an "avid swimmer," who used a swimming program to recover from a mild stroke late in her life. According to Rothschild, she had no eating disorder.

Vera-Ellen was married twice. Her first husband was a fellow dancer, Robert Hightower, to whom she was married from February 1941 to November 1946. Her second husband was oilman Victor Rothschild. They were married from 1954 to 1966 when they divorced. While married to Rothschild, she gave birth to a daughter, Victoria Ellen, who died in 1963 at three months from SIDS. Following the death of her only child, she withdrew from public life.

Death
Vera-Ellen died at the Los Angeles County General Hospital on August 30, 1981, of ovarian cancer. She was 60 years old.

Stage work

 * Very Warm for May (1939)
 * Higher and Higher (1940)
 * Panama Hattie (1940)
 * By Jupiter (1942)
 * A Connecticut Yankee (1943)

title: Vera-Ellen