A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915434063724544 |
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| author | Kim, KeeTaek Sano, Taketo |
| author_facet | Kim, KeeTaek Sano, Taketo |
| contents | We introduce a diagrammatic approach to Rasmussen's $s$-invariant, based on Bar-Natan's reformulation of Khovanov homology for tangles and cobordisms. This method enables a local computation of $s$ from a tangle decomposition of a knot diagram. As an application, we compute the $s$-invariants of all 3-strand pretzel knots. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05414 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms Kim, KeeTaek Sano, Taketo Geometric Topology 57K18 We introduce a diagrammatic approach to Rasmussen's $s$-invariant, based on Bar-Natan's reformulation of Khovanov homology for tangles and cobordisms. This method enables a local computation of $s$ from a tangle decomposition of a knot diagram. As an application, we compute the $s$-invariants of all 3-strand pretzel knots. |
| title | A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms |
| topic | Geometric Topology 57K18 |
| url | https://arxiv.org/abs/2503.05414 |