Mutation-invariance of Khovanov-Floer theories

Adam Saltz

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arXiv · 1806.05595

Mutation-invariance of Khovanov-Floer theories

Adam Saltz

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Abstract

Khovanov-Floer theories are a class of homological link invariants which admit spectral sequences from Khovanov homology. They include Khovanov homology, Szab{\'o}'s geometric link homology, singular instanton homology, and various Floer theories applied to branched double covers. In this short note we show that certain strong Khovanov-Floer theories, including Szab{\'o} homology and singular instanton homology, are invariant under Conway mutation. This confirms conjectures of Seed and Lambert-Cole. Along the way we prove two other conjectures about the structure of Szab{\'o} homology.

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Adam Saltz. 2018-06-14. Mutation-invariance of Khovanov-Floer theories. https://arxiv.org/abs/1806.05595

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