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 . 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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