oriented cobordism

Two oriented n-manifoldsMathworldPlanetmath M and M are called cobordant if there is an oriented n+1 manifold with boundary N such that N=MMopp where Mopp is M with orientation reversed. The triple (N,M,M) is called a oriented cobordism. Cobordism is an equivalence relationMathworldPlanetmath, and a very coarse invariant of manifolds. For example, all surfaces are cobordant to the empty setMathworldPlanetmath (and hence to each other).

There is a cobordism category, where the objects are manifolds, and the morphisms are cobordisms between them. This category is important in topological .

Title oriented cobordism
Canonical name OrientedCobordism
Date of creation 2013-03-22 13:56:05
Last modified on 2013-03-22 13:56:05
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 7
Author mathcam (2727)
Entry type Definition
Classification msc 57N70
Classification msc 57Q20
Synonym cobordant
Synonym bordism