Contact 3-manifolds twenty years since J. Martinet's work
Annales de l'Institut Fourier, Volume 42 (1992) no. 1-2, p. 165-192
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 .
L’article présente les récents développements de la géométrie des variétés de contact de dimension 3. Le théorème principal de ce papier donne l’existence d’une unique structure de contact tendue sur la sphère S 3 . Ce résultat complète la classification des structures de contact sur S 3 .
@article{AIF_1992__42_1-2_165_0,
     author = {Eliashberg, Yakov},
     title = {Contact 3-manifolds twenty years since J. Martinet's work},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {42},
     number = {1-2},
     year = {1992},
     pages = {165-192},
     doi = {10.5802/aif.1288},
     mrnumber = {93k:57029},
     zbl = {0756.53017},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_1992__42_1-2_165_0}
}
Contact 3-manifolds twenty years since J. Martinet's work. Annales de l'Institut Fourier, Volume 42 (1992) no. 1-2, pp. 165-192. doi : 10.5802/aif.1288. https://aif.centre-mersenne.org/item/AIF_1992__42_1-2_165_0/

[Be] D. Bennequin, Entrelacements et equations de Pfaff, Astérique, 107-108 (1983), 83-61. | MR 86e:58070 | Zbl 0573.58022

[Ce] J. Cerf, Sur les difféomorphismes de S3 (Г = 0), Lect. Notes in Math., 53 (1968). | MR 37 #4824 | Zbl 0164.24502

[E1] Y. Eliashberg, Classification of overtwisted contact structures on 3-manifolds, Invent. Math., 98 (1989), 623-637. | MR 90k:53064 | Zbl 0684.57012

[E2] Y. Eliashberg, The complexification of contact structures on a 3-manifold, Usp. Math. Nauk., 6(40) (1985), 161-162. | Zbl 0601.53029

[E3] Y. Eliashberg, On symplectic manifolds with some contact properties, J. Diff. Geometry, 33 (1991), 233-238. | MR 92g:57036 | Zbl 0735.53021

[E4] Y. Eliashberg, Filling by holomorphic discs and its applications, London Math. Soc. Lect. Notes Ser., 151 (1991), 45-67. | MR 93g:53060 | Zbl 0731.53036

[E5] Y. Eliashberg, Topological characterization of Stein manifolds of dimension > 2, Int. J. of Math., 1, n°1 (1990), 29-46. | MR 91k:32012 | Zbl 0699.58002

[E6] Y. Eliashberg, New invariants of open symplectic and contact manifolds, J. Amer. Math. Soc., 4 (1991), 513-520. | MR 92c:58030 | Zbl 0733.58011

[E7] Y. Eliashberg, Legendrian and transversal knots in tight contact manifolds, preprint, 1991.

[EG] Y. Eliashberg and M. Gromov, Convex symplectic manifolds, Proc. of Symposia in Pure Math., 52 (1991), part 2, 135-162. | MR 93f:58073 | Zbl 0742.53010

[Gi] E. Giroux, Convexité en topologie de contact, to appear in Comm. Math. Helvet., 1991. | MR 93b:57029 | Zbl 0766.53028

[Gro] M. Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math., 82 (1985), 307-347. | MR 87j:53053 | Zbl 0592.53025

[HE] V. Harlamov and Y. Eliashberg, On the number of complex points of a real surface in a complex surface, Proc. LITC-82, (1982), 143-148. | Zbl 0609.32016

[Lu] R. Lutz, Structures de contact sur les fibre's principaux en cercles de dimension 3, Ann. Inst. Fourier, 27-3 (1977), 1-15. | Numdam | MR 57 #17668 | Zbl 0328.53024

[Ma] J. Martinet, Formes de contact sur les variétés de dimension 3, Lect. Notes in Math, 209 (1971), 142-163. | MR 50 #3263 | Zbl 0215.23003

[McD] D. Mcduff, The structure of rational and ruled symplectic 4-manifolds, J. Amer. Math. Soc., 3, n°1 (1990), 679-712. | MR 91k:58042 | Zbl 0723.53019