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## Sutured TQFT, torsion, and tori

### Abstract

We use the theory of sutured TQFT to classify contact elements in the sutured Floer homology, with $\Z$ coefficients, of certain sutured manifolds of the form $(\Sigma \times S^1, F \times S^1)$ where $\Sigma$ is an annulus or punctured torus. Using this classification, we give a new proof that the contact invariant in sutured Floer homology with $\Z$ coefficients of a contact structure with Giroux torsion vanishes. We also give a new proof of Massot's theorem that the contact invariant vanishes for a contact structure on $(\Sigma \times S^1, F \times S^1)$ described by an isolating dividing set.Comment: 29 pages, 16 figure

Topics: Mathematics - Symplectic Geometry, Mathematics - Geometric Topology, 57M50 (Primary), 57R56, 57R58 (Secondary)
Year: 2011
OAI identifier: oai:arXiv.org:1102.3450
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