Tight contact structures on some small Seifert fibered 3--manifolds
Abstract
We classify tight contact structures on the small Seifert fibered 3--manifold M(-1; r1, r2, r3) with ri in (0,1) and r1, r2 ≥ 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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