  Ozsvath-Szabo contact invariants are a powerful way to prove tightness of
contact structures but they are known to vanish in the presence of Giroux
torsion. In this paper we construct, on infinitely many manifolds, infinitely
many isotopy classes of universally tight torsion free contact structures whose
Ozsvath-Szabo invariant vanishes. We also discuss the relation between these
invariants and an invariant on T^3 and construct other examples of new
phenomena in Heegaard--Floer theory. Along the way, we prove two conjectures of
K Honda, W Kazez and G Matic about their contact topological quantum field
theory. Almost all the proofs in this paper rely on their gluing theorem for
sutured contact invariants.
