Surfaces of infinite-type are non-Hopfian
We show that finite-type surfaces are characterized by a topological analogue of the Hopf property. Namely, an oriented surface $\Sigma $ is of finite-type if and only if every proper map $f\colon \,\Sigma \rightarrow \Sigma $ of degree one is homotopic to a homeomorphism.
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-10-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.504/ |
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| author | Das, Sumanta Gadgil, Siddhartha |
| author_facet | Das, Sumanta Gadgil, Siddhartha |
| author_sort | Das, Sumanta |
| collection | DOAJ |
| description | We show that finite-type surfaces are characterized by a topological analogue of the Hopf property. Namely, an oriented surface $\Sigma $ is of finite-type if and only if every proper map $f\colon \,\Sigma \rightarrow \Sigma $ of degree one is homotopic to a homeomorphism. |
| format | Article |
| id | doaj-art-d84e747060b9466a8b1845e88d54dfab |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-10-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-d84e747060b9466a8b1845e88d54dfab2025-02-07T11:10:23ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-10-01361G81349135610.5802/crmath.50410.5802/crmath.504Surfaces of infinite-type are non-HopfianDas, Sumanta0Gadgil, Siddhartha1Department of Mathematics, Indian Institute of Science, Bangalore 560012, IndiaDepartment of Mathematics, Indian Institute of Science, Bangalore 560012, IndiaWe show that finite-type surfaces are characterized by a topological analogue of the Hopf property. Namely, an oriented surface $\Sigma $ is of finite-type if and only if every proper map $f\colon \,\Sigma \rightarrow \Sigma $ of degree one is homotopic to a homeomorphism.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.504/ |
| spellingShingle | Das, Sumanta Gadgil, Siddhartha Surfaces of infinite-type are non-Hopfian Comptes Rendus. Mathématique |
| title | Surfaces of infinite-type are non-Hopfian |
| title_full | Surfaces of infinite-type are non-Hopfian |
| title_fullStr | Surfaces of infinite-type are non-Hopfian |
| title_full_unstemmed | Surfaces of infinite-type are non-Hopfian |
| title_short | Surfaces of infinite-type are non-Hopfian |
| title_sort | surfaces of infinite type are non hopfian |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.504/ |
| work_keys_str_mv | AT dassumanta surfacesofinfinitetypearenonhopfian AT gadgilsiddhartha surfacesofinfinitetypearenonhopfian |