Topologie de contact en dimension 3 [autour des travaux de Yakov Eliashberg]

Giroux, Emmanuel

Séminaire Bourbaki : volume 1992/93, exposés 760-774, Astérisque, no. 216 (1993), Exposé no. 760, 27 p.

MR 1246390 | Zbl 0793.53037 | 7 citations dans Numdam

BibTeX
RIS

@incollection{SB_1992-1993__35__7_0,
     author = {Giroux, Emmanuel},
     title = {Topologie de contact en dimension 3 [autour des travaux de {Yakov} {Eliashberg]}},
     booktitle = {S\'eminaire Bourbaki : volume 1992/93, expos\'es 760-774},
     author = {Collectif},
     series = {Ast\'erisque},
     note = {talk:760},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {216},
     year = {1993},
     zbl = {0793.53037},
     mrnumber = {1246390},
     language = {fr},
     url = {http://archive.numdam.org/item/SB_1992-1993__35__7_0/}
}

TY  - CHAP
AU  - Giroux, Emmanuel
TI  - Topologie de contact en dimension 3 [autour des travaux de Yakov Eliashberg]
BT  - Séminaire Bourbaki : volume 1992/93, exposés 760-774
AU  - Collectif
T3  - Astérisque
N1  - talk:760
PY  - 1993
DA  - 1993///
IS  - 216
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/SB_1992-1993__35__7_0/
UR  - https://zbmath.org/?q=an%3A0793.53037
UR  - https://www.ams.org/mathscinet-getitem?mr=1246390
LA  - fr
ID  - SB_1992-1993__35__7_0
ER  -

Giroux, Emmanuel. Topologie de contact en dimension 3 [autour des travaux de Yakov Eliashberg], dans Séminaire Bourbaki : volume 1992/93, exposés 760-774, Astérisque, no. 216 (1993), Exposé no. 760, 27 p. http://archive.numdam.org/item/SB_1992-1993__35__7_0/

Bibliographie
Cité par

[Al] S. Altschuler, A linear contact flow for 3-dimensional manifolds, prépublication (Camberra) 1991.

[Ar1] V. I. Arnold, Méthodes mathématiques de la mécanique classique, Mir 1974. | MR 474391 | Zbl 0385.70001

[Ar2] V. I. Arnold, Singularities of caustics and wave fronts, Kluwer 1990. | MR 1151185 | Zbl 0734.53001

[Ar3] V. I. Arnold, Contact geometry and wave propagation, L'Ens. Math. 36 (1990), 215-266. | MR 1096419 | Zbl 0715.53002

[Ar4] V. I. Arnold, Contact geometry : the geometrical method of Gibbs's thermodynamics, Proc. of the Gibbs Symp., D.G. Caldi et G.D. Mostow eds, Amer. Math. Soc. (1990), 163-179. | MR 1095332 | Zbl 0737.53029

[Ar5] V. I. Arnold, Chapitres supplémentaires de la théorie des équations différentielles ordinaires, Mir 1978. | MR 361232 | Zbl 0956.34502

[Au] M. Audin, Cobordisme d'immersions lagrangiennes et legendriennes, Travaux en Cours 20, Hermann 1987. | Zbl 0615.57001

[Ben1] D. Bennequin, Entrelacements et équations de Pfaff, Soc. Math. France, Astérisque 107-108 (1983), 83-161. | MR 753131 | Zbl 0573.58022

[Ben2] D. Bennequin, Topologie symplectique, convexité holomorphe et structures de contact [d'après Ya. Eliashberg, D. McDuff et al.], Sém. Bourbaki exposé 725, Soc. Math. France, Astérisque 189-190 (1990), 285-323. | Numdam | MR 1099880 | Zbl 0755.32009

[BFG] M. Beals, C. Fefferman et R. Grossman, Strictly pseudo-convex domains in Cn, Bull. Amer. Math. Soc. 89 (1983), 125-322. | MR 684898 | Zbl 0546.32008

[Bl] D. Blair, Contact manifolds in Riemannian geometry, Springer Lect. Notes in Math. 509 (1976). | MR 467588 | Zbl 0319.53026

[CaCo] J. C. Cantwell et L. W. Conlon, Poincaré-Bendixson's theory for leaves of codimension 1, Trans. Amer. Math. Soc. 265 (1981), 181-209. | MR 607116 | Zbl 0484.57015

[Ch] S. S. Chern, The geometry of G-structures, Bull. Amer. Math. Soc. 72 (1966), 167-219. | MR 192436 | Zbl 0136.17804

[Dav] A. A. Davydov, Normal forms of differential equations, unresolved in derivative, Funct. Anal. Appl. 19 (1985), 1-10. | MR 800916 | Zbl 0582.34056

[Dou] A. Douady, Nœuds et structures de contact en dimension 3 [d'après D. Bennequin], Sém. Bourbaki exposé 604, Soc. Math. France, Astérisque 105-106 (1983), 129-148. | Numdam | Zbl 0522.53034

[El1] Ya. Eliashberg, Classification of overtwisted contact structures on 3-manifolds, Invent. Math. 98 (1989), 623-637. | MR 1022310 | Zbl 0684.57012

[El2] Ya. Eliashberg, Contact 3-manifolds, twenty years since J. Martinet's work, Ann. Inst. Fourier 42 (1992), 165-192. | Numdam | MR 1162559 | Zbl 0756.53017

[El3] Ya. Eliashberg, New invariants of open symplectic and contact manifolds, J. Amer. Math. Soc. 4 (1991), 513-520. | MR 1102580 | Zbl 0733.58011

[El4] Ya. Eliashberg, Filling by holomorphic discs and its applications, London Math. Soc. Lect. Notes Ser. 151 (1991), 45-67. | MR 1171908 | Zbl 0731.53036

[El5] Ya. Eliashberg, Legendrian and transversal knots in tight contact manifolds, à paraître dans le livre Topological methods in modern mathematics (en l'honneur de J. Milnor), Publish or Perish. | Zbl 0809.53033

[El6] Ya. Eliashberg, communication orale privée sur des travaux récents de W. Thurston (Luminy), mai 1992.

[El7] Ya. Eliashberg, Topological characterization of Stein manifolds of dimension > 2, Int. J. of Math. 1 (1990), 29-46. | MR 1044658 | Zbl 0699.58002

[El8] Ya. Eliashberg, On symplectic manifolds with some contact properties, J. Diff. Geom. 33 (1991), 233-238. | MR 1085141 | Zbl 0735.53021

[ElGr] Ya. Eliashberg et M. Gromov, Convex symplectic manifolds, Proc. of Symp. in Pure Math. 52 (1991), 135-162. | MR 1128541 | Zbl 0742.53010

[Ga] D. Gabai, Foliations and the topology of 3-manifolds, J. Diff. Geom. 18 (1983), 445-503. | MR 723813 | Zbl 0533.57013

[Gei] H. Geiges, Contact structures on (n - 1)-connected (2n + 1)-manifolds, Pacific J. of Math (à paraître). | MR 1237141 | Zbl 0791.53039

[Gi1] E. Giroux, Convexité en topologie de contact, Comment. Math. Helv. 66 (1991), 637-677. | MR 1129802 | Zbl 0766.53028

[Gi2] E. Giroux, Une structure de contact, même tendue, est plus ou moins tordue, Ann. Scient. Ec. Norm. Sup. (à paraître). | Numdam | Zbl 0819.53018

[Gra] J. W. Gray, Some global properties of contact structures, Ann. of Math. 69 (1959), 421-450. | MR 112161 | Zbl 0092.39301

[Gro1] M. Gromov, Stable maps of foliations into manifolds, Izv. Akad. Nauk. S.S.S.R. 33 (1969), 707 734. | MR 263103 | Zbl 0197.20404

[Gro2] M. Gromov, Pseudo-holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347. | MR 1554036 | Zbl 0592.53025

[Gro3] M. Gromov, Partial differential relations, Springer Verlag 1986. | MR 864505 | Zbl 0651.53001

[GuRo] R. Gunning et H. Rossi, Analytic functions of several complex variables, Prentice Hall 1965. | MR 180696 | Zbl 0141.08601

[He] G. Hector, Architecture des feuilletages de classe C2, Soc. Math. France, Astérisque 107-108 (1983), 243-258. | MR 753140 | Zbl 0533.57014

[Hu] S. Humphries, Generators for the mapping class group, Springer Lect. Notes in Math. 722 (1979), 44-47. | MR 547453 | Zbl 0732.57004

[LaSi] F. Lalonde et J.-C. Sikorav, Sous-variétés lagrangiennes et lagrangiennes exactes des fibrés cotangents, Comment. Math. Helv. 66 (1991), 18-33. | MR 1090163 | Zbl 0759.53022

[Le] G. Levitt, Feuilletages des variétés de dimension 3 qui sont des fibrés en cercles, Comment. Math. Helv. 53 (1978), 572-594. | MR 511848 | Zbl 0393.57004

[Lu1] R. Lutz, Sur quelques propriétés des formes différentielles en dimension 3, thèse (Strasbourg) 1971.

[Lu2] R. Lutz, Structures de contact sur les fibrés principaux en cercles de dimension 3, Ann. Inst. Fourier 27 (1977), 1-15. | Numdam | MR 478180 | Zbl 0328.53024

[Lu3] R. Lutz, Sur la géométrie des structures de contact invariantes, Ann. Inst. Fourier 29 (1979), 283-303. | Numdam | MR 526789 | Zbl 0379.53011

[Ma] J. Martinet, Formes de contact sur les variétés de dimension 3, Springer Lect. Notes in Math. 209 (1971), 142-163. | MR 350771 | Zbl 0215.23003

[McD1] D. Mcduff, Applications of convex integration to symplectic and contact geometry, Ann. Inst. Fourier 37 (1987), 107-133. | Numdam | MR 894563 | Zbl 0572.58010

[McD2] D. Mcduff, The structure of rational and ruled symplectic 4-manifolds, J. Amer. Math. Soc. 3 (1990), 679-712. | MR 1049697 | Zbl 0723.53019

[Me] C. Meckert, Forme de contact sur la somme connexe de deux variétés de contact de dimension impaire, Ann. Inst. Fourier 32 (1982), 251-260. | Numdam | MR 688029 | Zbl 0471.58001

[Mo] J. Moser, On the volume element of a manifold, Trans. Amer. Math. Soc. 120 (1965), 286-294. | MR 182927 | Zbl 0141.19407

[Mul] M.-P. Muller, Une structure symplectique sur R6 avec une sphère lagrangienne plongée et un champ de Liouville complet, Comment. Math. Helv. 65 (1990), 623-663. | MR 1078102 | Zbl 0716.53037

[Mum] D. Mumford, Abelian quotients of the Teichmüller modular group, J. d'Anal. Math. 18 (1967), 227-244. | MR 219543 | Zbl 0173.22903

[Po] J. Powell, Two theorems on the mapping class group of a surface, Proc. Amer. Math. Soc. 68 (1978), 347-350. | MR 494115 | Zbl 0391.57009

[Ros] H. Rosenberg, Foliations by planes, Topology 7 (1968), 131-138. | MR 228011 | Zbl 0157.30504

[Rou] R. Roussarie, Plongements dans les variétés feuilletées et classification de feuilletages sans holonomie, Publ. Math. I.H.E.S. 43 (1973), 101-142. | Numdam | MR 358809 | Zbl 0356.57017

[Ru] M. Rumin, Formes différentielles sur les variétés de contact, thèse (Orsay) 1992.

[Si1] J.-C. Sikorav, Rigidité symplectique dans le cotangent de Tn, Duke Math. J. 59 (1989), 227-231. | MR 1046748 | Zbl 0697.53035

[Si2] J.-C. Sikorav, Quelques propriétés des plongements lagrangiens, Suppl. Bull. Soc. Math. France, Mem. No 46, 119 (1991), 151-167. | Numdam | MR 1125841 | Zbl 0751.58010

[Su] D. Sullivan, A homological characterization of foliations consisting of minimal surfaces, Comment. Math. Helv. 54 (1979), 218-223. | MR 535056 | Zbl 0409.57025

[Th1] W. Thurston, Foliations of manifolds which are circle-bundles, thèse (Berkeley) 1972.

[Th2] W. Thurston, A norm for the homology of 3-manifolds, Mem. Amer. Math. Soc. 339 (1986), 99 130. | MR 823443 | Zbl 0585.57006

[Th3] W. Thurston, Contact structures and foliations on 3-manifolds, exposé oral à la West Coast Topology Conf. (Stanford), mai 1992.

[ThWi] W. Thurston et H. Winkelnkemper, On the existence of contact forms, Proc. Amer. Math. Soc. 52 (1975), 345-347. | MR 375366 | Zbl 0312.53028

[We] A. Weinstein, Contact surgeries and symplectic handlebodies, Hokkaido Math. J. 20 (1991), 241-251. | MR 1114405 | Zbl 0737.57012