#### Volume 7, issue 3 (2007)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Subscriptions Author Index To Appear Contacts ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
Contact Ozsváth–Szabó invariants and Giroux torsion

### Paolo Lisca and András I Stipsicz

Algebraic & Geometric Topology 7 (2007) 1275–1296
##### 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 $\left(Y,\xi \right)$ has positive Giroux torsion then there exists a Stein cobordism from $\left(Y,\xi \right)$ to a contact 3–manifold $\left(Y,{\xi }^{\prime }\right)$ such that $\left(Y,\xi \right)$ is obtained from $\left(Y,{\xi }^{\prime }\right)$ by a Lutz modification.

##### Keywords
contact structures, Giroux torsion, Ozsváth–Szabó invariants, fillable contact structures, symplectic fillability
Primary: 57R17
Secondary: 57R57