Khovanov homology and equivariant surfaces
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909694780506112 |
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| author | Borodzik, Maciej Dai, Irving Mallick, Abhishek Stoffregen, Matthew |
| author_facet | Borodzik, Maciej Dai, Irving Mallick, Abhishek Stoffregen, Matthew |
| contents | We introduce a refinement of Bar-Natan homology for involutive links, extending the work of Lobb-Watson and Sano. We construct a new suite of numerical invariants and derive bounds for the genus of equivariant cobordisms between strongly invertible knots. Our invariants show that the difference between the equivariant slice genus and isotopy-equivariant slice genus can be arbitrarily large, whereas previously these were not known to differ. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13642 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Khovanov homology and equivariant surfaces Borodzik, Maciej Dai, Irving Mallick, Abhishek Stoffregen, Matthew Geometric Topology 57K18, 57M60 We introduce a refinement of Bar-Natan homology for involutive links, extending the work of Lobb-Watson and Sano. We construct a new suite of numerical invariants and derive bounds for the genus of equivariant cobordisms between strongly invertible knots. Our invariants show that the difference between the equivariant slice genus and isotopy-equivariant slice genus can be arbitrarily large, whereas previously these were not known to differ. |
| title | Khovanov homology and equivariant surfaces |
| topic | Geometric Topology 57K18, 57M60 |
| url | https://arxiv.org/abs/2507.13642 |