A simplification problem in manifold theory
| Autor: | Hausmann, Jean-Claude, Jahren, Bjørn |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 35 pages. Small corrections and improvements following referee's suggestions. To appear in "L'Enseignement Math\'ematique" |
| Databáze: | arXiv |
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