manifold torus

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• Manifold — For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two dimensional manifold since it can be represented by a collection of two dimensional maps. In mathematics (specifically in differential geometry and topology),… …   Wikipedia

• Torus bundle — In mathematics, in the sub field of geometric topology, a torus bundle is a kind of surface bundle over the circle, which in turn are a class of three manifolds.ConstructionTo obtain a torus bundle: let f be an orientation preserving… …   Wikipedia

• Torus — Not to be confused with Taurus (disambiguation). This article is about the surface and mathematical concept of a torus. For other uses, see Torus (disambiguation). A torus As the distance to th …   Wikipedia

• Torus knot — In knot theory, a torus knot is a special kind of knot which lies on the surface of an unknotted torus in R3. Similarly, a torus link is a link which lies on the surface of a torus in the same way. Each torus knot is specified by a pair of… …   Wikipedia

• Manifold decomposition — In topology, a branch of mathematics, a manifold M may be decomposed or split by writing M as a combination of smaller pieces. When doing so, one must specify both what those pieces are and how they are put together to form M. Manifold… …   Wikipedia

• Whitehead manifold — In mathematics, the Whitehead manifold is an open 3 manifold that is contractible, but not homeomorphic to R3. Henry Whitehead discovered this puzzling object while he was trying to prove the Poincaré conjecture.A contractible manifold is one… …   Wikipedia

• Calabi–Yau manifold — In mathematics, Calabi ndash;Yau manifolds are compact Kähler manifolds whose canonical bundle is trivial. They were named Calabi ndash;Yau spaces by physicists in 1985, [cite journal | author = Candelas, Horowitz, Strominger and Witten | year =… …   Wikipedia

• Riemannian manifold — In Riemannian geometry, a Riemannian manifold ( M , g ) (with Riemannian metric g ) is a real differentiable manifold M in which each tangent space is equipped with an inner product g in a manner which varies smoothly from point to point. The… …   Wikipedia

• 3-manifold — In mathematics, a 3 manifold is a 3 dimensional manifold. The topological, piecewise linear, and smooth categories are all equivalent in three dimensions, so little distinction is usually made in whether we are dealing with say, topological 3… …   Wikipedia

• Lefschetz manifold — In mathematics, a Lefschetz manifold is a particular kind of symplectic manifold.DefinitionsLet M be a (2n) dimensional smooth manifold. Each element: [omega] in H {DR}^2 (M) of the second de Rham cohomology space of M induces a map :L { [omega]… …   Wikipedia

• Topological manifold — In mathematics, a topological manifold is a Hausdorff topological space which looks locally like Euclidean space in a sense defined below. Topological manifolds form an important class of topological spaces with applications throughout… …   Wikipedia