Contact 3-manifolds twenty years since J. Martinet's work

  • Eliashberg Y
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Abstract

Twenty years ago Jean Martinet (see [Ma]) showed that any orientable closed 3-manifold admits a contact structure. Three years later after the work of R. Lutz (see [4]) and in the wake of the triumph of Gromov's h-principle, it seemed that the classification of closed contact 3-manifolds was at hand. Ten years later in the seminal work [Be], D. Bennequin showed that the situation is much more complicated and that the classification of contact structures on 3-manifolds, and even on S' 3 , was not likely to be achieved. My paper [El] raised the hope that the situation is not so bad. The subject of the present paper is the status of the problem today and some recent progress in this direction including the classification of contact structures on 5 3 . I discussed the original plan of this paper with D. Bennequin, I got further inspiration from the work [Gi] of E. Giroux and from numerous

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Eliashberg, Y. (1992). Contact 3-manifolds twenty years since J. Martinet’s work. Annales de l’institut Fourier, 42(1–2), 165–192. https://doi.org/10.5802/aif.1288

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