Contact Ozsvath-Szabo Invariants and Giroux Torsion

Details Contact Ozsvath-Szabo Invariants and Giroux Torsion Contact Ozsvath-Szabo Invariants and Giroux Torsion

2006-04-12

arxiv.org/abs/math/0604268v3

Mathematics

Symplectic Geometry

22 pages, 5 figures; rephrased abstract and introduction

Scientific paper

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,\xi) has positive Giroux torsion then there exists a Stein cobordism from (Y,\xi) to a contact 3--manifold (Y,\xi') such that (Y,\xi) is obtained from (Y,\xi') by a Lutz modification.

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