Seifert fibered contact three-manifolds via surgery

Abstract

Using contact surgery we define families of contact structures on certain Seifert fibered three–manifolds. We prove that all these contact structures are tight using contact Ozsváth–Szabó invariants. We use these examples to show that, given a natural number $n$, there exists a Seifert fibered three–manifold carrying at least $n$ pairwise non-isomorphic tight, not fillable contact structures.