Heegaard Floer homologies and contact structures

2002/10/08 by Peter Ozsváth, Peter Ozsvath, Zoltán Szabó +3 · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Symplectic Geometry (math.SG) #math.GT #math.SG #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0210127

22 pages, 3 figures

arxiv created 2002/10/08 · openalex publication_date 2002/10/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a contact structure on a closed, oriented three-manifold Y, we describe an invariant which takes values in the three-manifold's Floer homology \HFa. This invariant vanishes for overtwisted contact structures and is non-zero for Stein fillable ones. The construction uses of Giroux's interpretation of contact structures in terms of open book decompositions, and the knot Floer homologies introduced in math.GT/0209056.

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• Khovanov homology and tight contact structures

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