Tight contact structures on some small Seifert fibered 3--manifolds

Details Tight contact structures on some small Seifert fibered 3--manifolds Tight contact structures on some small Seifert fibered 3--manifolds

2005-09-30

arxiv.org/abs/math/0509714v1

Mathematics

Symplectic Geometry

38 pages, 10 figures

Scientific paper

We classify tight contact structures on the small Seifert fibered 3--manifold M(-1; r_1, r_2, r_3) with r_i in (0,1) and r_1, r_2 \geq 1/2. The result is obtained by combining convex surface theory with computations of contact Ozsvath--Szabo invariants. We also show that some of the tight contact structures on the manifolds considered are nonfillable, justifying the use of Heegaard Floer theory.

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