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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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