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

Lisca, Paolo¹ ; Stipsicz, András I²

¹ Dipartimento di Matematica, Università di Pisa, I-56127 Pisa, Italy
² Rényi Institute of Mathematics, Hungarian Academy of Sciences, H-1053 Budapest, Reáltanoda utca 13–15, Hungary

Geometry & topology, Tome 7 (2003) no. 2, pp. 1055-1073.

Résumé

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.

Détail

DOI : 10.2140/gt.2003.7.1055

Keywords: tight, fillable, contact structures

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