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Quelques propriétés globales des variétés différentiables

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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.

Contents

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

3.

4. Cobordant sub-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.