Contact Ozsváth–Szabó invariants and Giroux torsion

Lisca, Paolo; Stipsicz, Andras I

doi:10.2140/agt.2007.7.1275

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Contact Ozsváth–Szabó invariants and Giroux torsion

Paolo Lisca and András I Stipsicz

Algebraic & Geometric Topology 7 (2007) 1275–1296

DOI: 10.2140/agt.2007.7.1275

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 $(Y, ξ)$ has positive Giroux torsion then there exists a Stein cobordism from $(Y, ξ)$ to a contact 3–manifold $(Y, ξ^{'})$ such that $(Y, ξ)$ is obtained from $(Y, ξ^{'})$ by a Lutz modification.

Keywords

contact structures, Giroux torsion, Ozsváth–Szabó invariants, fillable contact structures, symplectic fillability

Mathematical Subject Classification 2000

Primary: 57R17

Secondary: 57R57

References

Publication

Received: 7 December 2006

Accepted: 17 August 2007

Published: 24 September 2007

Authors

Paolo Lisca
Dipartimento di Matematica “L. Tonelli” Università di Pisa Largo Bruno Pontecorvo, 5 I-56127 Pisa Italy

András I Stipsicz
Rényi Institute of Mathematics Hungarian Academy of Sciences H-1053 Budapest Reáltanoda utca 13–15 Hungary

Volume 7, issue 3 (2007)