Bar-Natan’s deformation of Khovanov homology and involutive monopole Floer homology

Abstract

We study the conjugation involution in Seiberg–Witten theory in the context of Ozsvath–Szabo and Bloom’s spectral sequence for the branched double cover of a link L in $$S^3.$$ We prove that there exists a spectral sequence of $$\mathbb {F}[Q]/Q^2$$ -modules (where Q has degree $$-1$$ ) which converges to $$\widetilde{ HMI }_*(\Sigma (L)),$$ an involutive version of the monopole Floer homology of the branched double cover, and whose $$E^2$$ -page is a version of Bar-Natan’s deformation of Khovanov homology in characteristic two of the mirror of L.