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Heegaard Floer homologies and contact structures

Peter Ozsvath·Zoltan Szabo
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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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Peter Ozsvath, Zoltan Szabo. 2002-10-08. Heegaard Floer homologies and contact structures. https://arxiv.org/abs/math/0210127

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