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.