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 -action on Heegaard Floer homology. We show that on homology the -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