Heegaard Floer Homology and Balanced Presentations of Groups

Abstract

Let $G$ be a group with a finite balanced presentation $P$. We associate a Heegaard Floer homology group ${\widehat{HF}}_P(G)$ with the pair $(G,P)$ based on some extra choices and technical assumptions. We show that ${\widehat{HF}}_P(G)$ is independent from these choices and also is invariant under stable Andrews-Curtis transformations on $P$, based on two claims which are not settled in this paper.

This paper's results were based on two claims. However, we later identified an issue with those claims. We addressed this and improved our findings in two subsequent papers: arXiv:2109.13844 and arXiv:2205.14706