English

Graph cobordisms and Heegaard Floer homology

Geometric Topology 2026-03-25 v3

Abstract

We construct a graph TQFT for the minus flavor of Heegaard Floer homology. Our graph TQFT extends Ozsv\'{a}th and Szab\'{o}'s TQFT for closed and connected 3-manifolds, and allows for cobordisms with disconnected ends. As an application, we give an explicit formula for the chain homotopy type of the π1\pi_1-action on Heegaard Floer homology. We show that on homology the π1\pi_1-action is trivial on the plus, minus and infinity flavors, but give examples where it is non-trivial on the hat flavor.

Keywords

Cite

@article{arxiv.1512.01184,
  title  = {Graph cobordisms and Heegaard Floer homology},
  author = {Ian Zemke},
  journal= {arXiv preprint arXiv:1512.01184},
  year   = {2026}
}

Comments

108 pages. Numerous improvements to the presentation. Several aspects of the construction have been streamlined