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Eliashberg, Yakov

Contact 3-manifolds twenty years since J. Martinet’s work. (English) Zbl 0756.53017

Ann. Inst. Fourier 42, No. 1-2, 165-192 (1992).
The paper gives an account of the recent development in 3-dimensional contact geometry. The central result of the paper states that there exists a unique tight contact structure on \(S^ 3\). Together with the earlier classification of overtwisted contact structures on 3-manifolds this result completes the classification of contact structures on \(S^ 3\).
Reviewer: Y.Eliashberg (Stanford)

Cited in 10 Reviews
Cited in 158 Documents

MSC:

53D35 Global theory of symplectic and contact manifolds
57M50 General geometric structures on low-dimensional manifolds
53D10 Contact manifolds (general theory)
57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53-02 Research exposition (monographs, survey articles) pertaining to differential geometry

Keywords:

contact geometry; tight contact structure; overtwisted contact structures; 3-manifolds
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References:

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