Equivariant Unknotting Number and Involutive Khovanov Homology
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914463213420544 |
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| author | Kim, KeeTaek |
| author_facet | Kim, KeeTaek |
| contents | We demonstrate that the equivariant unknotting number $\widetilde{u}(K)$ of a strongly invertible knot $K$ is bounded below by the $H$-torsion order $\widetilde{\mathrm{ord}}(K)$ of the involutive Bar-Natan homology $\widetilde{\mathrm{BN}}(K)$. This result serves as an equivariant analogue to the bound established by Alishahi. As an application, we identify five strongly invertible prime knots with crossing numbers at most $9$ for which the strict inequality $u(K) < \widetilde{u}(K)$ holds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08981 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equivariant Unknotting Number and Involutive Khovanov Homology Kim, KeeTaek Geometric Topology 57K10, 57K18 (Primary) 57M60 (Secondary) We demonstrate that the equivariant unknotting number $\widetilde{u}(K)$ of a strongly invertible knot $K$ is bounded below by the $H$-torsion order $\widetilde{\mathrm{ord}}(K)$ of the involutive Bar-Natan homology $\widetilde{\mathrm{BN}}(K)$. This result serves as an equivariant analogue to the bound established by Alishahi. As an application, we identify five strongly invertible prime knots with crossing numbers at most $9$ for which the strict inequality $u(K) < \widetilde{u}(K)$ holds. |
| title | Equivariant Unknotting Number and Involutive Khovanov Homology |
| topic | Geometric Topology 57K10, 57K18 (Primary) 57M60 (Secondary) |
| url | https://arxiv.org/abs/2604.08981 |