Geometry & Topology, Vol. 7 (2003) Paper no. 30, pages 1055--1073.

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

Paolo Lisca Andras I Stipsicz

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, 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.

Keywords. Tight, fillable, contact structures

AMS subject classification. Primary: 57R57. Secondary: 57R17.

DOI: 10.2140/gt.2003.7.1055

E-print: arXiv:math.SG/0208063

Submitted to GT on 4 September 2002. Paper accepted 23 December 2003. Paper published 29 December 2003.

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Paolo Lisca Andras I Stipsicz
Dipartimento di Matematica, Universita di Pisa
I-56127 Pisa, ITALY
and
Renyi Institute of Mathematics, Hungarian Academy of Sciences
H-1053 Budapest, Realtanoda utca 13--15, Hungary

Email: lisca@dm.unipi.it, stipsicz@math-inst.hu

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