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

Ghiggini, Paolo; Lisca, Paolo; Stipsicz, Andras I.

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

Authors

Ghiggini, Paolo

Lisca, Paolo

Stipsicz, Andras I.

Description

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.
38 pages, 10 figures