Tight contact structures on some small Seifert fibered 3-manifolds

Abstract

We classify tight contact structures on the small Seifert fibered 3-manifolds M(−1; r1, r2, r3) with ri ∈ (0, 1) ∩ Q and r1, r2 ≥ ½ . The result is obtained by combining convex surface theory with computations of contact Ozsváth–Szabó invariants. We also show that some of the tight contact structures on the manifolds considered are nonfillable, justifying the use of Heegaard Floer theory.