Symmetries of equivariant Khovanov homology
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916941903429632 |
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| author | Khovanov, Mikhail Sano, Taketo |
| author_facet | Khovanov, Mikhail Sano, Taketo |
| contents | We study symmetries in equivariant versions of Khovanov homology, which include (i) the construction of an involution $\widehatσ$ for the $U(2)$-equivariant theory, (ii) an integral lifting $\widehatν$ of the Shumakovitch operation $ν$, and (iii) splitting of the $U(1)$- and $U(1)\times U(1)$-equivariant theories generalizing earlier work over $\mathbb{F}_2$. Finally, we relate these structures to the Rasmussen $s$-invariant over an arbitrary field $F$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03785 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetries of equivariant Khovanov homology Khovanov, Mikhail Sano, Taketo Quantum Algebra Geometric Topology 57K18, 57K16, 18N25 We study symmetries in equivariant versions of Khovanov homology, which include (i) the construction of an involution $\widehatσ$ for the $U(2)$-equivariant theory, (ii) an integral lifting $\widehatν$ of the Shumakovitch operation $ν$, and (iii) splitting of the $U(1)$- and $U(1)\times U(1)$-equivariant theories generalizing earlier work over $\mathbb{F}_2$. Finally, we relate these structures to the Rasmussen $s$-invariant over an arbitrary field $F$. |
| title | Symmetries of equivariant Khovanov homology |
| topic | Quantum Algebra Geometric Topology 57K18, 57K16, 18N25 |
| url | https://arxiv.org/abs/2509.03785 |