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Mathematische Annalen

, Volume 358, Issue 1–2, pp 351–359 | Cite as

Contact structures on \(M \times S^2\)

  • Jonathan Bowden
  • Diarmuid Crowley
  • András I. Stipsicz
Article

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 \(M \times T^2\).

Keywords

Manifold Boundary Component Contact Structure Contact Manifold Solid Torus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jonathan Bowden
    • 1
  • Diarmuid Crowley
    • 2
  • András I. Stipsicz
    • 3
  1. 1.Mathematisches InstitutUniversität AugsburgAugsburgGermany
  2. 2.Max Planck Institut für MathematikBonnGermany
  3. 3.Rényi Institute of MathematicsBudapestHungary

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