Abstract
We show that if a manifold \(M\) admits a contact structure, then so does \(M \times S^2\). Our proof relies on surgery theory, a theorem of Eliashberg on contact surgery and a theorem of Bourgeois showing that if \(M\) admits a contact structure then so does \(M \times T^2\).
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Acknowledgments
The authors would like to thank the Max Planck Institute for Mathematics in Bonn for its hospitality while parts of this work has been carried out, and Hansjörg Geiges for useful comments on an earlier draft of the paper. AS was partially supported by OTKA NK81203, by the Lendület program of the Hungarian Academy of Sciences and by ERC LDTBud. The present work is part of the authors’ activities within CAST, a Research Network Program of the European Science Foundation.
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Bowden, J., Crowley, D. & Stipsicz, A.I. Contact structures on \(M \times S^2\) . Math. Ann. 358, 351–359 (2014). https://doi.org/10.1007/s00208-013-0963-9
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DOI: https://doi.org/10.1007/s00208-013-0963-9