Gluing diffeomorphisms, bi-Lipschitz mappings and homeomorphisms
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917959027392512 |
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| author | Goldstein, Paweł Grochulska, Zofia Hajłasz, Piotr |
| author_facet | Goldstein, Paweł Grochulska, Zofia Hajłasz, Piotr |
| contents | Cerf and Palais independently proved a remarkable result about extending diffeomorphisms defined on smooth balls in a manifold to global diffeomorphisms of the manifold onto itself. We explain Palais' argument and show how to extend it to the class of homeomorphisms and bi-Lipschitz homeomorphisms. While Palais' argument is surprising, it is elementary and short. However, its extension to bi-Lipschitz homeomorphisms and homeomorphisms requires deep results: the stable homeomorphism and the annulus theorems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_13508 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gluing diffeomorphisms, bi-Lipschitz mappings and homeomorphisms Goldstein, Paweł Grochulska, Zofia Hajłasz, Piotr Geometric Topology Primary: 54C20 Secondary: 57N55, 58C07, 58C25 Cerf and Palais independently proved a remarkable result about extending diffeomorphisms defined on smooth balls in a manifold to global diffeomorphisms of the manifold onto itself. We explain Palais' argument and show how to extend it to the class of homeomorphisms and bi-Lipschitz homeomorphisms. While Palais' argument is surprising, it is elementary and short. However, its extension to bi-Lipschitz homeomorphisms and homeomorphisms requires deep results: the stable homeomorphism and the annulus theorems. |
| title | Gluing diffeomorphisms, bi-Lipschitz mappings and homeomorphisms |
| topic | Geometric Topology Primary: 54C20 Secondary: 57N55, 58C07, 58C25 |
| url | https://arxiv.org/abs/2404.13508 |