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

Details Ozsvath-Szabo invariants and tight contact three-manifolds, III Ozsvath-Szabo invariants and tight contact three-manifolds, III

2005-05-24

arxiv.org/abs/math/0505493v2

Mathematics

Symplectic Geometry

30 pages, 7 figures; some results improved, new results on planar contact structures added

Scientific paper

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.

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