Combinatorial Heegaard Floer homology and sign assignments

TL;DR

This paper introduces an integral version of combinatorial Heegaard Floer homology for nice diagrams and demonstrates that the independence proof adapts to this new setting.

Contribution

It provides an integral lift of the combinatorial Heegaard Floer homology and adapts the independence proof to this integral framework.

Findings

Established an integral lift of combinatorial Heegaard Floer homology.

Proved the independence of the homology under diagram modifications in the integral setting.

Abstract

We provide an intergral lift of the combinatorial definition of Heegaard Floer homology for nice diagrams, and show that the proof of independence using convenient diagrams adapts to this setting.