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Contact Ozsvath-Szabo Invariants and Giroux Torsion

Paolo Lisca·Andras I. Stipsicz
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Abstract

In this paper we prove a vanishing theorem for the contact Ozsvath--Szabo 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 the circle 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.

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Paolo Lisca, Andras I. Stipsicz. 2006-12-07. Contact Ozsvath-Szabo Invariants and Giroux Torsion. https://arxiv.org/abs/math/0604268

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