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

TL;DR

This paper introduces an integral lift of Szabó's spectral sequence starting from odd Khovanov homology, providing a new link homology framework that aligns with Szabó's original construction and allows for universal coefficient computations.

Contribution

It presents a novel integral chain complex lifting Szabó's spectral sequence from mod 2 to integral coefficients, connecting odd Khovanov homology to Szabó's link homology.

Findings

Provides an integral chain complex lifting Szabó's spectral sequence

Establishes a spectral sequence from odd Khovanov homology to Szabó's link homology

Enables computation of Szabó's link homology via the Universal Coefficient Theorem

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 Szab\'o has constructed such a lift independently (unpublished).