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An infinite family of tight, not semi-fillable contact three-manifolds. (English) Zbl 1127.57302
Summary: We prove that an infinite family of virtually overtwisted tight contact structures discovered by Honda on certain circle bundles over surfaces admit no symplectic semi-fillings. The argument uses results of Mrowka, Ozsváth and Yu on the translation-invariant solutions to the Seiberg-Witten equations on cylinders and the non-triviality of the Kronheimer-Mrowka monopole invariants of symplectic fillings.

MSC:
57R57 Applications of global analysis to structures on manifolds
57R17 Symplectic and contact topology in high or arbitrary dimension
53D35 Global theory of symplectic and contact manifolds
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