Graph cobordisms and Heegaard Floer homology

Zemke, Ian

doi:10.2140/gt.2026.30.389

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Graph cobordisms and Heegaard Floer homology

Ian Zemke

Geometry & Topology 30 (2026) 389–528

DOI: 10.2140/gt.2026.30.389

Abstract

We construct a graph TQFT for the minus flavor of Heegaard Floer homology. Our graph TQFT extends Ozsváth and Szabó’s TQFT for closed and connected 3-manifolds, and assigns maps to cobordisms with disconnected ends. As an application, we give an explicit formula for the chain homotopy type of the $π_{1}$ -action on Heegaard Floer homology. We show that on homology the $π_{1}$ -action is trivial on the plus, minus and infinity flavors, but give examples where it is nontrivial on the hat flavor.

Keywords

Heegaard Floer homology, cobordisms, TQFT, 4-manifolds, low-dimensional topology

Mathematical Subject Classification 2010

Primary: 57M27, 57R58

References

Publication

Received: 26 January 2016

Revised: 6 June 2019

Accepted: 20 September 2024

Published: 16 March 2026

Proposed: Peter Ozsváth

Seconded: Ciprian Manolescu, András I Stipsicz

Authors

Ian Zemke
Department of Mathematics Princeton University Princeton, NJ United States	Department of Mathematics University of Oregon Eugene, OR United States

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Volume 30, issue 2 (2026)