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arXiv · 2509.03785

Symmetries of equivariant Khovanov homology

Mikhail Khovanov·Taketo Sano
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Abstract

We study symmetries in equivariant versions of Khovanov homology, which include (i) the construction of an involution $\widehat{\sigma}$ for the $U(2)$-equivariant theory, (ii) an integral lifting $\widehat{\nu}$ of the Shumakovitch operation $\nu$, 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 $F$.

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Mikhail Khovanov, Taketo Sano. 2025-09-04. Symmetries of equivariant Khovanov homology. https://doi.org/10.4064/fm250906-26-2

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