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Filtering the Heegaard Floer contact invariant

Çağatay Kutluhan, Gordana Matić, Jeremy Van Horn-Morris and Andy Wand

Geometry & Topology 27 (2023) 2181–2236
Abstract

We define an invariant of contact structures in dimension three from Heegaard Floer homology. This invariant takes values in the set 0 {}. It is zero for overtwisted contact structures, for Stein-fillable contact structures, nondecreasing under Legendrian surgery, and computable from any supporting open book decomposition. As an application, we give an easily computable obstruction to Stein-fillability on closed contact 3–manifolds with nonvanishing Ozsváth–Szabó contact class.

Keywords
Heegaard Floer homology, contact structure
Mathematical Subject Classification 2010
Primary: 57R17
Secondary: 57R58
References
Publication
Received: 18 February 2020
Revised: 21 January 2022
Accepted: 13 March 2022
Published: 25 August 2023
Proposed: András I Stipsicz
Seconded: Ciprian Manolescu, Peter Ozsváth
Authors
Çağatay Kutluhan
Department of Mathematics
University at Buffalo
Buffalo, NY
United States
Gordana Matić
Department of Mathematics
University of Georgia
Athens, GA
United States
Jeremy Van Horn-Morris
Department of Mathematics
University of Arkansas
Fayetteville, AR
United States
Andy Wand
School of Mathematics and Statistics
University of Glasgow
Glasgow
United Kingdom

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