Title: Contact Ozsváth–Szabó invariants and Giroux torsion
Abstract: In this paper we prove a vanishing theorem for the contact Ozsváth-Szabó invariants of certain contact 3-manifolds having positive Giroux torsion.We use this result to establish similar vanishing results for contact structures with underlying 3-manifolds admitting either a torus fibration over S 1 or a Seifert fibration over an orientable base.We also show -using standard techniques from contact topology -that if a contact 3-manifold .Y; / has positive Giroux torsion then there exists a Stein cobordism from .Y; / to a contact 3-manifold .Y; 0 / such that .Y; / is obtained from .Y; 0 / by a Lutz modification.