Algebraic and Geometric Topology 1 (2001), paper no. 7, pages 153-172.

Symplectic fillability of tight contact structures on torus bundles

Fan Ding, Hansjorg Geiges

Abstract. We study weak versus strong symplectic fillability of some tight contact structures on torus bundles over the circle. In particular, we prove that almost all of these tight contact structures are weakly, but not strongly symplectically fillable. For the 3-torus this theorem was established by Eliashberg.

Keywords. Tight contact structure, weak and strong symplectic filling, contact surgery

AMS subject classification. Primary: 53D35. Secondary: 57M50, 57R65.

DOI: 10.2140/agt.2001.1.153

E-print: arXiv:math.SG/0104109

Submitted: 15 December 2000. (Revised: 13 February 2001.) Accepted: 13 February 2001. Published: 21 March 2001.

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Fan Ding, Hansjorg Geiges
Department of Mathematics, Peking University
Beijing 100871, P. R. China
Mathematisch Instituut, Universiteit Leiden
Postbus 9512, 2300 RA Leiden, Netherlands

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