2014/05/13 by John A. Baldwin, Steven Sivek · 2 citations
Mathematics · #Advanced Operator Algebra Research #Floer homology #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homology (biology) #Instanton #Invariant (physics) #Magnetic monopole #Regular polygon #math.GT #math.SG
paper · pdf · doi:10.1007/s00029-015-0206-x
published as Selecta Math. 22 (2016), no. 2, 939--978 · 32 pages, 7 figures; this paper was originally part of arXiv:1403.1930
arxiv created 2014/05/13 · openalex publication_date 2015/10/28 · arxiv updated 2016/03/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We define an invariant of contact 3-manifolds with convex boundary using Kronheimer and Mrowka's sutured instanton Floer homology theory. To the best of our knowledge, 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 the authors in [1].