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arxiv: 0807.2431 · v1 · submitted 2008-07-15 · 🧮 math.GT

Contact structures, sutured Floer homology and TQFT

classification 🧮 math.GT
keywords suturedcontactdimensionalfloergammagluinghomologymanifold
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We describe the natural gluing map on sutured Floer homology which is induced by the inclusion of one sutured manifold (M',\Gamma') into a larger sutured manifold (M,\Gamma), together with a contact structure on M-M'. As an application of this gluing map, we produce a (1+1)-dimensional TQFT by dimensional reduction and study its properties.

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  1. On symplectic fillings of spinal open book decompositions II: Holomorphic curves and classification

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    Contact 3-manifolds admitting uniform spinal open books with planar pages have their weak, strong, and exact symplectic and Stein fillings classified by diffeomorphism classes of Lefschetz fibrations.