Instanton Floer homology and contact structures

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• 作者：John A. Baldwin ; Steven Sivek
• 刊名：Selecta Mathematica, New Series
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：22
• 期：2
• 页码：939-978
• 全文大小：892 KB
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• 作者单位：John A. Baldwin (1)
  Steven Sivek (2)
  
  1. Department of Mathematics, Boston College, Chestnut Hill, MA, USA
  2. Department of Mathematics, Princeton University, Princeton, NJ, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-9020

文摘

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).