On mutation invariance in Khovanov homology

Artem Kotelskiy; Liam Watson; Claudius Zibrowius

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arXiv · 2602.23442

On mutation invariance in Khovanov homology

Artem Kotelskiy·Liam Watson·Claudius Zibrowius

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Abstract

We show that reduced Khovanov homology over any field is invariant under component-preserving Conway mutation. Our proof relies on strong geography restrictions for a certain Khovanov multicurve invariant associated with Conway tangles that we introduced in previous work [arXiv:1910.14584]. Applying ideas from homological mirror symmetry, we give a full classification of the components of this invariant.

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Artem Kotelskiy, Liam Watson, Claudius Zibrowius. 2026-02-26. On mutation invariance in Khovanov homology. https://arxiv.org/abs/2602.23442

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