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)

Abstract

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.
• Status: Published
• Refereed: Yes
• 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: 1465-3060
• 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

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
173046		Rigidity and flexibility in contact topology	Andrew Wand	Engineering and Physical Sciences Research Council (EPSRC)	EP/P004598/1	M&S - Mathematics