Contact Ozsváth–Szabó invariants and Giroux torsion

Lisca, Paolo¹ ; Stipsicz, Andras I²

¹Dipartimento di Matematica “L. Tonelli”, Università di Pisa, Largo Bruno Pontecorvo, 5, I-56127 Pisa, Italy
²Rényi Institute of Mathematics, Hungarian Academy of Sciences, H-1053 Budapest, Reáltanoda utca 13–15, Hungary

Algebraic and Geometric Topology, Tome 7 (2007) no. 3, pp. 1275-1296

Résumé

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.

Détail

DOI : 10.2140/agt.2007.7.1275

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

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