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, 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

References

Forward citations

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

Volume 7, issue 2 (2003)

Paolo Lisca and András I Stipsicz