Heegaard Floer homologies and contact structures

الأصل · EN

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.