Instanton Floer homology and contact structures

• John A. Baldwin ^[1] ; Steven Sivek ^[2]
  1. [1] Boston College

     Boston College

     City of Boston, Estados Unidos

     
  2. [2] Princeton University

     Princeton University

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 2, 2016, págs. 939-978
• Idioma: inglés
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• Resumen

  • 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