Odd Khovanov homology is mutation invariant

Abstract

We define a link homology theory that is readily seen to be both isomorphic to reduced odd Khovanov homology and fully determined by data impervious to Conway mutation. This gives an elementary proof that odd Khovanov homology is mutation invariant, and therefore that mod 2 Khovanov homology is mutation invariant. We also establish mutation invariance for the entire Ozsvath-Szabo spectral sequence from reduced Khovanov homology to the Heegaard Floer homology of the branched double cover.

8 pages, 4 figures (modified intro and remarks)

References in corpus (7)

• Mutant knots and intersection graphs
• A spanning tree model for the Heegaard Floer homology of a branched double-cover
• On the spectral sequence from Khovanov homology to Heegaard Floer homology
• Khovanov homology, open books, and tight contact structures
• Invariants of genus 2 mutants
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Cited by in corpus (8)

• Instantons and odd Khovanov homology
• Computations of the Lipshitz-Sarkar Steenrod Square on Khovanov Homology
• A link surgery spectral sequence in monopole Floer homology
• Mutation invariance of Khovanov homology over ${\mathbb{F}}_2$
• A remark on Khovanov homology and two-fold branched covers
• Extremal Khovanov homology of Turaev genus one links
• Computations of Szabó's Geometric Spectral Sequence in Khovanov Homology
• An Exceptional Splitting of Khovanov's Arc Algebras in Characteristic 2