Symmetries of equivariant Khovanov homology
Volume 274 / 2026
Fundamenta Mathematicae 274 (2026), 63-98
MSC: Primary 57K18; Secondary 18N25
DOI: 10.4064/fm250906-26-2
Published online: 25 June 2026
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 $F$.
