An integral lift, starting in odd Khovanov homology, of Szab\'o's spectral sequence

Abstract

Ozsv\'ath, Rasmussen and Szab\'o constructed odd Khovanov homology. It is a link invariant which has the same reduction modulo 2 as (even) Khovanov homology. Szab\'o introduced a spectral sequence with mod 2 coefficients from mod 2 Khovanov homology to another link homology. He got his spectral sequence from a chain complex with a filtration. We give an integral lift of Szab\'o's complex that provides a spectral sequence from odd Khovanov homology to a link homology, from which one can get Szab\'o's link homology with the Universal Coefficient Theorem. Szab\'o has constructed such a lift independently (unpublished).