A simplification problem in manifold theory

J. Hausmann, B. Jahren
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引用次数: 3

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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流形理论中的一个简化问题
如果两个光滑流形M和N与实线的乘积是微分同构的,则称它们为r -微分同构。我们考虑下面的化简问题:r -微同态意味着微同态还是同同态?对于紧流形,这个问题的分析依赖于流形理论的一些主要成果,特别是高维的h-和s-协同定理以及最近在3维和4维的惊人分类结果。本文介绍了关于r -微分同态的分类的一些新结果和目前对这一问题的认识。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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