Integral lift of Ozsváth–Szabó spectral sequence via odd Khovanov homology

Establish an integral spectral sequence from reduced odd Khovanov homology to the Heegaard–Floer homology of the branched double cover of a knot, thereby lifting the mod 2 Ozsváth–Szabó spectral sequence from reduced Khovanov homology to Heegaard–Floer homology.

Background

Ozsváth, Rasmussen, and Szabó discovered odd Khovanov homology while seeking an integral lift of their mod 2 spectral sequence from reduced Khovanov homology to Heegaard–Floer homology of the branched double cover. They conjectured that replacing reduced Khovanov homology with reduced odd Khovanov homology should yield the integral lift.

Confirming this integral spectral sequence would clarify the relationship between odd Khovanov homology and Heegaard–Floer theory and could unlock stronger topological applications.