Strong Topological Rigidity of Non-Compact Orientable Surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866912167601635328 |
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| author | Das, Sumanta |
| author_facet | Das, Sumanta |
| contents | We show that every orientable infinite-type surface is properly rigid as a consequence of a more general result. Namely, we prove that if a homotopy equivalence between any two non-compact orientable surfaces is a proper map, then it is properly homotopic to a homeomorphism, provided surfaces are neither the plane nor the punctured plane. Thus all non-compact orientable surfaces, except the plane and the punctured plane, are topologically rigid in a strong sense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_11194 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Strong Topological Rigidity of Non-Compact Orientable Surfaces Das, Sumanta Geometric Topology Algebraic Topology 57K20 (Primary), 55S37 (Secondary) We show that every orientable infinite-type surface is properly rigid as a consequence of a more general result. Namely, we prove that if a homotopy equivalence between any two non-compact orientable surfaces is a proper map, then it is properly homotopic to a homeomorphism, provided surfaces are neither the plane nor the punctured plane. Thus all non-compact orientable surfaces, except the plane and the punctured plane, are topologically rigid in a strong sense. |
| title | Strong Topological Rigidity of Non-Compact Orientable Surfaces |
| topic | Geometric Topology Algebraic Topology 57K20 (Primary), 55S37 (Secondary) |
| url | https://arxiv.org/abs/2111.11194 |