We characterize L-spaces which are Seifert fibered over the 2-sphere in terms of taut foliations, transverse foliations and transverse contact structures. We give a sufficient condition for certain contact Seifert fibered 3-manifolds with e_0=-1 to have nonzero contact Ozsvath--Szabo invariants. This yields an algorithm for deciding whether a given small Seifert fibered L-space carries a contact structure with nonvanishing contact Ozsvath--Szabo invariant. As an application, we prove the existence of tight contact structures on some 3-manifolds obtained by integral surgery along a positive torus knot in the 3-sphere. Finally, we prove planarity of every contact structure on small Seifert fibered L-spaces with e_0 bigger than or equal to -1, and we discuss some consequences.

Ozsvath-Szabo invariants and tight contact 3--manifolds, III

LISCA, PAOLO;
2007-01-01

Abstract

We characterize L-spaces which are Seifert fibered over the 2-sphere in terms of taut foliations, transverse foliations and transverse contact structures. We give a sufficient condition for certain contact Seifert fibered 3-manifolds with e_0=-1 to have nonzero contact Ozsvath--Szabo invariants. This yields an algorithm for deciding whether a given small Seifert fibered L-space carries a contact structure with nonvanishing contact Ozsvath--Szabo invariant. As an application, we prove the existence of tight contact structures on some 3-manifolds obtained by integral surgery along a positive torus knot in the 3-sphere. Finally, we prove planarity of every contact structure on small Seifert fibered L-spaces with e_0 bigger than or equal to -1, and we discuss some consequences.
Lisca, Paolo; Stipsicz, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/109888
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