The flip map and involutions on Khovanov homology

Daren Chen; Hongjian Yang

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arXiv · 2506.00824

The flip map and involutions on Khovanov homology

Daren Chen·Hongjian Yang

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Abstract

The flip symmetry on knot diagrams induces an involution on Khovanov homology. We prove that this involution is determined by its behavior on unlinks; in particular, it is the identity map when working over $\mathbb{F}_2$. This confirms a folklore conjecture on the triviality of the Viro flip map. As a corollary, we prove that the symmetries on the transvergent and intravergent diagrams of a strongly invertible knot induce the same involution on Khovanov homology. We also apply similar techniques to study the half sweep-around map.

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Daren Chen, Hongjian Yang. 2025-06-01. The flip map and involutions on Khovanov homology. https://arxiv.org/abs/2506.00824

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