Heegaard Floer homologies and contact structures

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.

22 pages, 3 figures

References in corpus (1)

• Holomorphic disks and knot invariants

Cited by in corpus (5)

• Planar open books and Floer homology
• Holomorphic disks and knot invariants
• Thurston norm, fibered manifolds and twisted Alexander polynomials
• Tight contact structures on some small Seifert fibered 3--manifolds
• Notes on the contact Ozsvath--Szabo invariants