nLab Quelques propriétés globales des variétés différentiables


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 MSO(n)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.


Chapter I – Properties of differentiable maps

1. Definitions

3. Pre-image of a sub-manifold

4. Pre-image of a sub-manifold under a t-regular map

Chapter II – Sub-manifolds and homology classes of a manifold

2. Complex associated to a closed subgroup of the orthogonal group

Chapter III – On a problem of Steenrod

Chapter IV – Cobordant differentiable manifolds


4. Cobordant sub-manifolds

5. A fundamental theorem

category: reference

Last revised on February 3, 2021 at 14:13:00. See the history of this page for a list of all contributions to it.