Bulletin of the American Mathematical Society· 2012
Notes on Topological Stability
- 313citations
- 2012year
Short summary
This paper aims to prove that topologically stable mappings form a dense subset of C(N, P) for finite dimensional manifolds N and P (with N compact).
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Key points
- The ultimate aim is to prove that topologically stable mappings form a dense subset of C(N, P) for compact N.
- The first chapter studies Thom-Whitney theory of stratified sets and stratified mappings.
- Thom's second isotopy lemma, presented in Section 11, provides conditions for topological equivalence of mappings.
AI-generated from the title and abstract; the full text is not read.
Abstract
These notes are part of the first chapter of a series of lectures given by the author in the spring of 1970. The ultimate aim of these notes will be to prove the theorem that the set of topologically stable mappings form a dense subset of C (N, P ) for any finite dimensional manifolds N and P where N is compact. The first chapter is a study of Thom-Whitney theory of stratified sets and stratified mappings. The connection of the material in these notes with the theorem on the density of topologically stable mappings appears in Section 11, where we give Thom's second isotopy lemma. This result gives sufficient conditions for two mappings to be topologically equivalent.
The authors' abstract, as published at the source. Bulletin of the American Mathematical Society, 2012 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics