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; 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

References in corpus (3)

• On the Floer homology of plumbed three-manifolds
• A Legendrian surgery presentation of contact 3-manifolds
• Heegaard Floer homologies and contact structures