2006/04/12 by Paolo Lisca, András I. Stipsicz, Lisca, Paolo +2 · 1 citation
Mathematics · #57R17 #57R57 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.GT #math.SG #msc:57R17 #msc:57R57
paper · pdf · doi:10.48550/arxiv.math/0604268
22 pages, 5 figures; rephrased abstract and introduction
openalex publication_date 2006/04/12 · arxiv created 2006/12/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.