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An infinite family of tight, not semi-fillable contact three-manifolds

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, Ozsvath 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.

preprint2004arXivOpen access
Paolo LiscaAndras I Stipsicz
math.SGmath.GT
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Paolo LiscaAndras I Stipsicz

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