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 (Σ × S1, F × S1) where Σ 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 (Σ × S1, F × S1) described by an isolating dividing set.