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

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

2002-08-08

arxiv.org/abs/math/0208063v2

Geom. Topol. 7(2003) 1055-1073

Mathematics

Symplectic Geometry

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper30.abs.html

Scientific paper

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.

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