Involutive Khovanov homology and equivariant knots

Taketo Sano

doi:10.2140/agt.2025.25.5059

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arXiv · 2404.08568

Involutive Khovanov homology and equivariant knots

Taketo Sano

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Abstract

For strongly invertible knots, we define an involutive version of Khovanov homology, and from it derive a pair of integer-valued invariants $(\underline{s}, \overline{s})$, 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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BibTeX RIS

Taketo Sano. 2024-04-12. Involutive Khovanov homology and equivariant knots. https://doi.org/10.2140/agt.2025.25.5059

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