# nLab Quelques propriétés globales des variétés différentiables

Contents

### Context

#### Cobordism theory

Concepts of cobordism theory

flavors of bordism homology theories/cobordism cohomology theories, their representing Thom spectra and cobordism rings:

bordism theory$\;$M(B,f) (B-bordism):

relative bordism theories:

algebraic:

This entry is about the article

on differential topology, proving Thom's theorem which identifies cobordism classes of normally oriented submanifolds with homotopy classes of maps into a universal Thom space $M SO(n)$.

Together with

or rather its belated exposition in

due to which Thom’s construction came to be mainly known as the Pontryagin-Thom construction, this lays the foundations of cobordism theory as such and as a tool in stable homotopy theory.

# Contents

## Chapter IV – Cobordant differentiable manifolds

### 5. A fundamental theorem

category: reference

Last revised on February 3, 2021 at 09:13:00. See the history of this page for a list of all contributions to it.