Calegari's homotopy 4-spheres from fibered knots are standard
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915022000619520 |
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| author | Cha, Jae Choon Kim, Min Hoon |
| author_facet | Cha, Jae Choon Kim, Min Hoon |
| contents | In 2009, Calegari constructed smooth homotopy 4-spheres from monodromies of fibered knots. We prove that all these are diffeomorphic to the standard 4-sphere. Our method uses 5-dimensional handlebody techniques and results on mapping class groups of 3-dimensional handlebodies. As an application, we present potential counterexamples to the smooth 4-dimensional Schoenflies conjecture which are related to the work of Casson and Gordon on fibered ribbon knots. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10051 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Calegari's homotopy 4-spheres from fibered knots are standard Cha, Jae Choon Kim, Min Hoon Geometric Topology In 2009, Calegari constructed smooth homotopy 4-spheres from monodromies of fibered knots. We prove that all these are diffeomorphic to the standard 4-sphere. Our method uses 5-dimensional handlebody techniques and results on mapping class groups of 3-dimensional handlebodies. As an application, we present potential counterexamples to the smooth 4-dimensional Schoenflies conjecture which are related to the work of Casson and Gordon on fibered ribbon knots. |
| title | Calegari's homotopy 4-spheres from fibered knots are standard |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2411.10051 |