Cobordism revives the intuitive idea of bounding harbored in the original work of Poincaré but later sacrificed in order to construct a viable theory based on simpicial complexes.
Wikipedia foundation.
Cobordism — A cobordism (W;M,N). 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 of a manifold. Two manifolds are cobordant if their disjoint… … Wikipedia
Cobordism theorem — may refer to: h cobordism theorem s cobordism theorem This disambiguation page lists mathematics articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended … Wikipedia
Complex cobordism — In mathematics, complex cobordism is a generalized cohomology theory related to cobordism of manifolds. Its spectrum is denoted by MU. It is an exceptionally powerful cohomology theory, but can be quite hard to compute, so often instead of using… … Wikipedia
H-cobordism — A cobordism W between M and N is an h cobordism if the inclusion maps : M hookrightarrow W quadmbox{and}quad N hookrightarrow Ware homotopy equivalences. If mbox{dim},M = mbox{dim},N = nand mbox{dim},W = n+1, it is called an n+1 dimensional h… … Wikipedia
Semi-s-cobordism — In mathematics, a cobordism ( W , M , M −) of an ( n + 1) dimensionsal manifold (with boundary) W between its boundary components, two n manifolds M and M − (n.b.: the original creator of this topic, Jean Claude Hausmann, used the notation M −… … Wikipedia
List of cohomology theories — This is a list of some of the ordinary and generalized (or extraordinary) homology and cohomology theories in algebraic topology that are defined on the categories of CW complexes or spectra. For other sorts of homology theories see the links at… … Wikipedia
Whitehead torsion — In mathematics, Whitehead torsion is an invariant of an h cobordism in a Whitehead group, that is important in simple homotopy theory and surgery theory. It is named for J. H. C. Whitehead.Whitehead torsionSuppose that W is an h cobordism from M… … Wikipedia
Atiyah–Singer index theorem — In the mathematics of manifolds and differential operators, the Atiyah–Singer index theorem states that for an elliptic differential operator on a compact manifold, the analytical index (closely related to the dimension of the space of solutions) … Wikipedia
Surgery theory — In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one manifold from another in a controlled way, introduced by Milnor (1961). Surgery refers to cutting out parts of the manifold… … Wikipedia
Akbulut cork — In topology an Akbulut cork is a structure is frequently used to show that in four dimensions, the smooth h cobordism theorem fails. It was named after Selman Akbulut.The basic idea of the Akbulut cork is that when attempting to use the h… … Wikipedia
