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

##### MSC:
 53D35 Global theory of symplectic and contact manifolds 57M50 General geometric structures on low-dimensional manifolds 53D10 Contact manifolds, general 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
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