A note on homotopy and pseudoisotopy of diffeomorphisms of $4$-manifolds
This note serves to record examples of diffeomorphisms of closed smooth $4$-manifolds $X$ that are homotopic but not pseudoisotopic to the identity, and to explain why there are no such examples when $X$ is orientable and its fundamental group is a free group.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.663/ |
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| _version_ | 1825206197834219520 |
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| author | Krannich, Manuel Kupers, Alexander |
| author_facet | Krannich, Manuel Kupers, Alexander |
| author_sort | Krannich, Manuel |
| collection | DOAJ |
| description | This note serves to record examples of diffeomorphisms of closed smooth $4$-manifolds $X$ that are homotopic but not pseudoisotopic to the identity, and to explain why there are no such examples when $X$ is orientable and its fundamental group is a free group. |
| format | Article |
| id | doaj-art-e68bef01cd304db98621112e268ba551 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-e68bef01cd304db98621112e268ba5512025-02-07T11:23:50ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G111515152010.5802/crmath.66310.5802/crmath.663A note on homotopy and pseudoisotopy of diffeomorphisms of $4$-manifoldsKrannich, Manuel0Kupers, Alexander1Department of Mathematics, Karlsruhe Institute of Technology, 76131 Karlsruhe, GermanyDepartment of Computer and Mathematical Sciences, University of Toronto Scarborough, 1265 Military Trail, Toronto, ON M1C 1A4, CanadaThis note serves to record examples of diffeomorphisms of closed smooth $4$-manifolds $X$ that are homotopic but not pseudoisotopic to the identity, and to explain why there are no such examples when $X$ is orientable and its fundamental group is a free group.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.663/4-Manifoldsdiffeomorphismspseudoisotopyhomotopysurgery theory |
| spellingShingle | Krannich, Manuel Kupers, Alexander A note on homotopy and pseudoisotopy of diffeomorphisms of $4$-manifolds Comptes Rendus. Mathématique 4-Manifolds diffeomorphisms pseudoisotopy homotopy surgery theory |
| title | A note on homotopy and pseudoisotopy of diffeomorphisms of $4$-manifolds |
| title_full | A note on homotopy and pseudoisotopy of diffeomorphisms of $4$-manifolds |
| title_fullStr | A note on homotopy and pseudoisotopy of diffeomorphisms of $4$-manifolds |
| title_full_unstemmed | A note on homotopy and pseudoisotopy of diffeomorphisms of $4$-manifolds |
| title_short | A note on homotopy and pseudoisotopy of diffeomorphisms of $4$-manifolds |
| title_sort | note on homotopy and pseudoisotopy of diffeomorphisms of 4 manifolds |
| topic | 4-Manifolds diffeomorphisms pseudoisotopy homotopy surgery theory |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.663/ |
| work_keys_str_mv | AT krannichmanuel anoteonhomotopyandpseudoisotopyofdiffeomorphismsof4manifolds AT kupersalexander anoteonhomotopyandpseudoisotopyofdiffeomorphismsof4manifolds AT krannichmanuel noteonhomotopyandpseudoisotopyofdiffeomorphismsof4manifolds AT kupersalexander noteonhomotopyandpseudoisotopyofdiffeomorphismsof4manifolds |