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Gordana Matic : Contact invariant in sutured Floer homology and fillability

In the 70's Thurston and Winkelnkemper showed how an open book decomposition of a 3-manifold can be used to construct a contact structure. In 2000 Giroux showed that every contact structure on a 3-manifold can be obtained from that process. Ozsvath and Szabo used this fact to define an invariant of contact structures in their Heegaard Floer homology, providing an important new tool to study contact 3-manifolds. In joint work with Ko Honda and Will Kazez we describe a simple way to visualize this contact invariant and provide a generalization and some applications. When the contact manifold has boundary, we define an invariant of contact structure living in sutured Floer homology, a variant of Heegaard Floer homology for a manifold with boundary due to Andras Juhasz. We describe a natural gluing map on sutured Floer homology and show how it produces a (1+1)-dimensional TQFT leading to new obstructions to fillability.

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