Sutured TQFT, torsion, and tori

Details Sutured TQFT, torsion, and tori Sutured TQFT, torsion, and tori

2011-02-16

arxiv.org/abs/1102.3450v1

Mathematics

Symplectic Geometry

29 pages, 16 figures

Scientific paper

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.

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