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Periodica Mathematica Hungarica

, Volume 73, Issue 1, pp 16–26 | Cite as

Symplectic fillability of toric contact manifolds

  • Aleksandra MarinkovićEmail author
Article

Abstract

According to Lerman, compact connected toric contact 3-manifolds with a non-free toric action whose moment cone spans an angle greater than \(\pi \) are overtwisted, thus non-fillable. In contrast, we show that all compact connected toric contact manifolds in dimension greater than three are weakly symplectically fillable and many of them are strongly symplectically fillable. The proof is based on Lerman’s classification of toric contact manifolds and on our observation that the only contact manifolds in higher dimensions that admit free toric action are the cosphere bundle of \(T^d, d\ge 3\,(T^d\times S^{d-1})\) and \(T^2\times L_k,\,k\in \mathbb {N}\), with the unique contact structure.

Keywords

Contact manifold Toric action Symplectic fillability 

Notes

Acknowledgments

I would like to thank Professors Miguel Abreu, Gustavo Granja, Klaus Niederkrüger, Milena Pabiniak and Branislav Prvulović for many useful disscussions. Moreover I thank the anonymous referees for their comments which have significantly improved an earlier version of this paper. My research was supported by the Fundação para a Ciência e a Tecnologia (FCT, Portugal) Grant SFRH/BD/77639/2011 and project PTDC/MAT/117762/2010.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2016

Authors and Affiliations

  1. 1.Center for Mathematical Analysis, Geometry and Dynamical Systems, Mathematics Department, Instituto Superior TécnicoUniversidade de Lisboa Av. Rovisco PaisLisboaPortugal

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