no. 1-2
Contact 3-manifolds twenty years since J. Martinet's work
Annales de l'Institut Fourier, Tome 42 (1992) no. 1-2, pp. 165-192.

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 .

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 .

@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},
     pages = {165--192},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {42},
     number = {1-2},
     year = {1992},
     doi = {10.5802/aif.1288},
     mrnumber = {93k:57029},
     zbl = {0756.53017},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1288/}
}
TY  - JOUR
AU  - Eliashberg, Yakov
TI  - Contact 3-manifolds twenty years since J. Martinet's work
JO  - Annales de l'Institut Fourier
PY  - 1992
SP  - 165
EP  - 192
VL  - 42
IS  - 1-2
PB  - Institut Fourier
PP  - Grenoble
UR  - http://www.numdam.org/articles/10.5802/aif.1288/
DO  - 10.5802/aif.1288
LA  - en
ID  - AIF_1992__42_1-2_165_0
ER  - 
%0 Journal Article
%A Eliashberg, Yakov
%T Contact 3-manifolds twenty years since J. Martinet's work
%J Annales de l'Institut Fourier
%D 1992
%P 165-192
%V 42
%N 1-2
%I Institut Fourier
%C Grenoble
%U http://www.numdam.org/articles/10.5802/aif.1288/
%R 10.5802/aif.1288
%G en
%F AIF_1992__42_1-2_165_0
Eliashberg, Yakov. Contact 3-manifolds twenty years since J. Martinet's work. Annales de l'Institut Fourier, Tome 42 (1992) no. 1-2, pp. 165-192. doi : 10.5802/aif.1288. http://www.numdam.org/articles/10.5802/aif.1288/

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

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

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

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

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

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

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

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

[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 | Zbl

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

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

[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

[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 | Zbl

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

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

Cité par Sources :