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Contact forms on 1-connected 5-manifolds

Published online by Cambridge University Press:  26 February 2010

C. B. Thomas
Affiliation:
Department of Mathematics, University College London.
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Extract

The even dimensional C manifold M2n is said to be symplectic, if there exists a 2-form Ω, defined everywhere on M such that

(i)Ω is closed, that is dΩ, = 0, and

(ii)Ωn ≠ 0.

Type
Research Article
Copyright
Copyright © University College London 1977

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References

1.A'Campo, N., “Feuilletages de codimension 1 sur les variétés simplement connexes de dimension 5”, Comm. Math. Hel., 47 (1972), 514525.CrossRefGoogle Scholar
2.Barden, D.. “Simply connected five manifolds”, Ann. of Math., 82 (1965), 365385.CrossRefGoogle Scholar
3.Durfee, A. and Lawson, B.. “Fibred knots and foliations of highly connected manifolds”, Inventiones math., 17 (1972), 203215.CrossRefGoogle Scholar
4.Godbillon, C.. Géométrie différentielle et mecanique analytique, (Hermann, Paris, 1969).Google Scholar
5.Gray, J. W.. “Some global properties of contact structures”, Annals of Math., 69 (1959), 421450.CrossRefGoogle Scholar
6.Haefliger, A.. Lectures on the theorem of Gromov, Proceedings of Liverpool Singularities Symposium II, Lecture Notes 209 (Springer-Verlag, 1971), 128141.Google Scholar
7.Thomas, C.. “Almost regular contact structures,” in Jour, of Diff. Geometry, 11 (1976) 521533.Google Scholar
8.Thurston, W. and Winkelnkemper, E.. “On the existence of contact forms”, (preprint).Google Scholar