Instanton Floer homology and contact structures

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Title: Instanton Floer homology and contact structures
Authors: Baldwin, JA
Sivek, S
Item Type: Journal Article
Abstract: We define an invariant of contact 3-manifolds with convex boundary using Kronheimer and Mrowka’s sutured instanton Floer homology theory. This is the first invariant of contact manifolds—with or without boundary—defined in the instanton Floer setting. We prove that our invariant vanishes for overtwisted contact structures and is nonzero for contact manifolds with boundary which embed into Stein fillable contact manifolds. Moreover, we propose a strategy by which our contact invariant might be used to relate the fundamental group of a closed contact 3-manifold to properties of its Stein fillings. Our construction is inspired by a reformulation of a similar invariant in the monopole Floer setting defined by Baldwin and Sivek (arXiv:1403.1930, 2014).
Issue Date: 28-Oct-2015
Date of Acceptance: 1-Oct-2015
DOI: 10.1007/s00029-015-0206-x
ISSN: 1022-1824
Publisher: Springer
Start Page: 939
End Page: 978
Journal / Book Title: Selecta Mathematica
Volume: 22
Issue: 2
Keywords: math.SG
0101 Pure Mathematics
General Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences

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