# Cobordism of smooth maps

From Diffgeom

Revision as of 02:08, 28 February 2008 by Vipul (talk | contribs) (New page: ==Definition== Suppose <math>M_1, M_2, P</math> are differential manifolds, and <math>f_1:M_1 \to P, f_2:M_2 \to P</math> are smooth maps. Then, a smooth cobordism from <math>f_1<...)

## Definition

Suppose are differential manifolds, and are smooth maps. Then, a smooth cobordism from to is the following data:

- A smooth cobordism from to i.e. a manifold with boundary with a diffeomorphism
- A smooth map such that the composite of with the inclusions of are respectively the maps

Note that we may sometimes fix the cobordism between and , and ask whether we can *fill in* a function for the particular cobordism.