A spanning tree cohomology theory for links

TL;DR

This paper introduces a new link invariant derived from a spectral sequence connecting Khovanov and Heegaard-Floer homologies, with a focus on proving its invariance and providing computational examples.

Contribution

It proves that the $E_3$-term of a spectral sequence, interpreted combinatorially, is a link invariant, advancing the understanding of link cohomology theories.

Findings

The $E_3$-term is a link invariant.

Provides explicit computations of the invariant.

Connects combinatorial and topological link invariants.

Abstract

In their recent preprint, Baldwin, Ozsv\'{a}th and Szab\'{o} defined a twisted version (with coefficients in a Novikov ring) of a spectral sequence, previously defined by Ozsv\'{a}th and Szab\'{o}, from Khovanov homology to Heegaard-Floer homology of the branched double cover along a link. In their preprint, they give a combinatorial interpretation of the $E_3$-term of their spectral sequence. The main purpose of the present paper is to prove directly that this $E_3$-term is a link invariant. We also give some concrete examples of computation of this invariant.