Filtering the Heegaard Floer contact invariant

Kutluhan, C., Matic, G., Van Horn Morris, J. and Wand, A. (2023) Filtering the Heegaard Floer contact invariant. Geometry and Topology, 27(6), pp. 2181-2236. (doi: 10.2140/gt.2023.27.2181)

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We define an invariant of contact structures in dimension three from Heegaard Floer homology. This invariant takes values in the set Z≥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.

Item Type:Articles
Additional Information:Kutluhan was supported in part by NSF grant DMS-1360293 and Simons Foundation grant 519352. Matic was supported in part by Simons Foundation grant 246461 and NSF ´ grant DMS-1664567. Van Horn-Morris was supported in part by Simons Foundation grants 279342 and 639259 and NSF grant DMS-1612412. Wand was supported in part by ERC grant GEODYCON and EPSRC EP/P004598/1.
Glasgow Author(s) Enlighten ID:Wand, Dr Andy
Authors: Kutluhan, C., Matic, G., Van Horn Morris, J., and Wand, A.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Geometry and Topology
Publisher:Mathematical Sciences Publishers
ISSN (Online):1364-0380
Copyright Holders:Copyright © 2023 MSP (Mathematical Sciences Publishers)
First Published:First published in Geometry and Topology 27(6):2181-2236
Publisher Policy:Reproduced under a Creative Commons licence

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
173046Rigidity and flexibility in contact topologyAndrew WandEngineering and Physical Sciences Research Council (EPSRC)EP/P004598/1M&S - Mathematics