Heegaard Floer Homology and Balanced Presentations of Groups

Neda Bagherifard; Nasser Boroojerdian

Heegaard Floer Homology and Balanced Presentations of Groups

Geometric Topology 2024-10-29 v2

Authors: Neda Bagherifard , Nasser Boroojerdian

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.

Keywords

heegaard floer homology balanced presentation group theory andrews-curtis transformations topology

Cite

@article{arxiv.1810.07939,
  title  = {Heegaard Floer Homology and Balanced Presentations of Groups},
  author = {Neda Bagherifard and Nasser Boroojerdian},
  journal= {arXiv preprint arXiv:1810.07939},
  year   = {2024}
}

Comments

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

Heegaard Floer Homology and Balanced Presentations of Groups

Abstract

Keywords

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