Involutive Khovanov homology and equivariant knots

Sano, Taketo

doi:10.2140/agt.2025.25.5059

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ISSN (electronic): 1472-2739

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Involutive Khovanov homology and equivariant knots

Taketo Sano

Algebraic & Geometric Topology 25 (2025) 5059–5111

DOI: 10.2140/agt.2025.25.5059

Abstract

For strongly invertible knots, we define an involutive version of Khovanov homology, and from it derive a pair of integer-valued invariants $(\underline{s}, \bar{s})$ , which is an equivariant version of Rasmussen’s $s$ -invariant. Using these invariants, we reprove that the infinite family of knots $J_{n}$ introduced by Hayden each admits exotic pairs of slice disks. Our construction is intended to give a Khovanov-theoretic analogue of the formalism given by Dai, Mallick and Stoffregen in involutive knot Floer theory.

Keywords

Khovanov homology, strongly invertible knots, equivariant knots

Mathematical Subject Classification

Primary: 57K18

References

Publication

Received: 4 May 2024

Revised: 22 November 2024

Accepted: 30 December 2024

Published: 20 November 2025

Authors

Taketo Sano
Interdisciplinary Theoretical and Mathematical Sciences Program RIKEN Wako Japan

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Volume 25, issue 8 (2025)