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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
An infinite family of tight, not semi-fillable contact three-manifolds

Paolo Lisca and András I Stipsicz

Geometry & Topology 7 (2003) 1055–1073

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 2000
Primary: 57R57
Secondary: 57R17
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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
Paolo Lisca
Dipartimento di Matematica
Università di Pisa
I-56127 Pisa
Italy
András I Stipsicz
Rényi Institute of Mathematics
Hungarian Academy of Sciences
H-1053 Budapest
Reáltanoda utca 13–15
Hungary