Geometry & Topology 7 (2003) 1055–1073

DOI: 10.2140/gt.2003.7.1055

arXiv: math.SG/0208063

Abstract

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.

Keywords

tight, fillable, contact structures

Mathematical Subject Classification

Primary: 57R57

Secondary: 57R17

References

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Publication

Received: 4 September 2002
Accepted: 23 December 2003
Published: 29 December 2003
Proposed: Tomasz Mrowka
Seconded: Yasha Eliashberg, John Morgan

Authors