Involutive Khovanov homology and equivariant knots

2024/04/12 by Taketo Sano, Sano, Taketo · 1 citation
Mathematics · Medicine · #57K18 #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2404.08568

openalex publication_date 2024/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For strongly invertible knots, we define an involutive version of Khovanov homology, and from it derive a pair of integer-valued invariants (\underlines, 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.

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