On the Khovanov homology of 3-braids
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909821920346112 |
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| author | Schuetz, Dirk |
| author_facet | Schuetz, Dirk |
| contents | We prove the conjecture of Przytycki and Sazdanovic that the Khovanov homology of the closure of a 3-stranded braid only contains torsion of order 2. This conjecture has been known for six out of seven classes in the Murasugi-classification of 3-braids and we show it for the remaining class. Our proof also works for the other classes and relies on Bar-Natan's version of Khovanov homology for tangles as well as his delooping and cancellation techniques, and the reduced integral Bar-Natan--Lee--Turner spectral sequence. We also show that the Knight-move conjecture holds for 3-braids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11547 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Khovanov homology of 3-braids Schuetz, Dirk Geometric Topology 57K18 (Primary) 57K10 (Secondary) We prove the conjecture of Przytycki and Sazdanovic that the Khovanov homology of the closure of a 3-stranded braid only contains torsion of order 2. This conjecture has been known for six out of seven classes in the Murasugi-classification of 3-braids and we show it for the remaining class. Our proof also works for the other classes and relies on Bar-Natan's version of Khovanov homology for tangles as well as his delooping and cancellation techniques, and the reduced integral Bar-Natan--Lee--Turner spectral sequence. We also show that the Knight-move conjecture holds for 3-braids. |
| title | On the Khovanov homology of 3-braids |
| topic | Geometric Topology 57K18 (Primary) 57K10 (Secondary) |
| url | https://arxiv.org/abs/2501.11547 |