A simplification problem in manifold theory

Jean-Claude Hausmann; Bjørn Jahren

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arXiv · 1802.03186

A simplification problem in manifold theory

Jean-Claude Hausmann·Bjørn Jahren

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Abstract

Two smooth manifolds M and N are called R-diffeomorphic if their product with the real line are diffeomorphic. We consider the following simplification problem: does R-diffeomorphism imply diffeomorphism or homeomorphism? For compact manifolds, analysis of this problem relies on some of the main achievements of the theory of manifolds, in particular the h- and s-cobordism theorems in high dimensions and the spectacular more recent classification results in dimensions 3 and 4. This paper presents what is currently known about the subject as well as some new results about classifications of R-diffeomorphisms.

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BibTeX RIS

Jean-Claude Hausmann, Bjørn Jahren. 2018-02-09. A simplification problem in manifold theory. https://arxiv.org/abs/1802.03186

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