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Seifert fibered contact three-manifolds via surgery. (English) Zbl 1064.57028
The authors use contact surgery to define families of contact structures on certain Seifert fibered manifolds. Using Ozsváth-Szabó invariants they show that all these contact structures are tight. Given $$n\in \mathbb N$$ they use Seiberg-Witten equations to show that some of the families contain at least $$n$$ pairwise non-isomorphic tight contact structures that are not symplectically fillable. The authors conjecture that a stronger fact is true. Namely that for the constructed families of tight contact structures all the contact structures in a family are pairwise non-isomorphic and all of them are symplectically non-fillable. In the case where the Seifert fibered manifold is $$M(g, 2g; (\alpha, 1))$$ with $$g\geq 1$$, the authors prove the conjecture for some $$\alpha\in \mathbb N$$.

##### MSC:
 57R17 Symplectic and contact topology in high or arbitrary dimension 57R57 Applications of global analysis to structures on manifolds 57N10 Topology of general $$3$$-manifolds (MSC2010) 57M50 General geometric structures on low-dimensional manifolds
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