A spectral sequence in odd Khovanov homology (Eine Spektralsequenz in ungerader Khovanov-Homologie)

TL;DR

This paper introduces a spectral sequence connecting odd Khovanov homology to another link homology, providing an integral lift of Szabo's complex, which enhances understanding of link invariants in knot theory.

Contribution

It constructs an integral lift of Szabo's spectral sequence, linking odd Khovanov homology to a new link homology, expanding the tools for studying link invariants.

Findings

Provides an integral lift of Szabo's complex.

Establishes a spectral sequence from odd Khovanov homology.

Connects odd Khovanov homology to a new link homology via spectral sequence.

Abstract

Ozsvath, Rasmussen and Szabo constructed odd Khovanov homology. It is a link invariant which has the same reduction modulo 2 as (even) Khovanov homology. Szabo 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 Szabo's complex, that provides a spectral sequence from odd Khovanov homology to a link homology, from which one can get Szabo's link homology with the Universal Coefficient Theorem. Szabo has constructed such a lift independently, but has not yet published it. This is my master thesis which I wrote under supervision of Thomas Schick at Georg August University G\"ottingen in summer 2011. It is in German. I will publish a reworked version in English later.