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On the existence of contact forms


Authors: W. P. Thurston and H. E. Winkelnkemper
Journal: Proc. Amer. Math. Soc. 52 (1975), 345-347
MSC: Primary 58A10; Secondary 57D30
DOI: https://doi.org/10.1090/S0002-9939-1975-0375366-7
MathSciNet review: 0375366
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Abstract: Using an old theorem of Alexander, we give a short and elementary proof that every closed, orientable $ 3$-manifold has a contact form.


References [Enhancements On Off] (What's this?)

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  • [4] J. W. Gray, Some global properties of contact structures, Ann. of Math. (2) 69 (1959), 421-450. MR 22 #3016. MR 0112161 (22:3016)
  • [5] H. B. Lawson, Jr., Foliations, Bull. Amer. Math. Soc. 80 (1974), 369-418. MR 0343289 (49:8031)
  • [6] R. Lutz, Sur quelques propriétés des formes différentielles en dimension trois, Thèse, Strasbourg, 1971.
  • [7] J. Martinet, Formes de contact sur les variétés de dimension $ 3$, Proc. Liverpool Singularities Sympos. II, Lecture Notes in Math., vol. 209, Springer-Verlag, Berlin and New York, 1971, 142-163. MR 0350771 (50:3263)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0375366-7
Article copyright: © Copyright 1975 American Mathematical Society

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