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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 \(\alpha\in \mathbb N\).

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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