Bordered Floer homology, handlebody detection, and compressing diffeomorphisms
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916563481788416 |
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| author | Alishahi, Akram Lipshitz, Robert |
| author_facet | Alishahi, Akram Lipshitz, Robert |
| contents | We show that, up to connected sums with integer homology $L$-spaces, bordered Floer homology detects handlebodies, as well as whether a mapping class extends over a given handlebody or compression body. Using this, we combine ideas of Casson-Long with the theory of train tracks to give an algorithm using bordered Floer homology to detect whether a mapping class extends over any compression body. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06619 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bordered Floer homology, handlebody detection, and compressing diffeomorphisms Alishahi, Akram Lipshitz, Robert Geometric Topology We show that, up to connected sums with integer homology $L$-spaces, bordered Floer homology detects handlebodies, as well as whether a mapping class extends over a given handlebody or compression body. Using this, we combine ideas of Casson-Long with the theory of train tracks to give an algorithm using bordered Floer homology to detect whether a mapping class extends over any compression body. |
| title | Bordered Floer homology, handlebody detection, and compressing diffeomorphisms |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2408.06619 |