Volume 7, issue 3 (2007)

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Contact Ozsváth–Szabó invariants and Giroux torsion

Paolo Lisca and András I Stipsicz

Algebraic & Geometric Topology 7 (2007) 1275–1296

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 S1 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.

contact structures, Giroux torsion, Ozsváth–Szabó invariants, fillable contact structures, symplectic fillability
Mathematical Subject Classification 2000
Primary: 57R17
Secondary: 57R57
Received: 7 December 2006
Accepted: 17 August 2007
Published: 24 September 2007
Paolo Lisca
Dipartimento di Matematica “L. Tonelli”
Università di Pisa
Largo Bruno Pontecorvo, 5
I-56127 Pisa
András I Stipsicz
Rényi Institute of Mathematics
Hungarian Academy of Sciences
H-1053 Budapest
Reáltanoda utca 13–15