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Heegaard Floer homology and contact structures

2005; Duke University Press; Volume: 129; Issue: 1 Linguagem: Inglês

10.1215/s0012-7094-04-12912-4

1547-7398

Peter Ozsváth, Zoltán Szabó,

Homotopy and Cohomology in Algebraic Topology

Given a contact structure on a closed, oriented three-manifold Y , we describe an invariant that takes values in the three-manifold's Floer homology HF ˆ . This invariant vanishes for overtwisted contact structures and is nonzero for Stein-fillable ones. The construction uses Giroux's interpretation of contact structures in terms of open-book decompositions.