@incollection{SB_2000-2001__43__345_0, author = {Skandalis, Georges}, title = {G\'eom\'etrie non commutative, op\'erateur de signature transverse et alg\`ebres de {Hopf}}, booktitle = {S\'eminaire Bourbaki : volume 2000/2001, expos\'es 880-893}, author = {Collectif}, series = {Ast\'erisque}, note = {talk:892}, publisher = {Soci\'et\'e math\'ematique de France}, number = {282}, year = {2002}, zbl = {1035.58007}, mrnumber = {1975185}, language = {fr}, url = {http://archive.numdam.org/item/SB_2000-2001__43__345_0/} }
TY - CHAP AU - Skandalis, Georges TI - Géométrie non commutative, opérateur de signature transverse et algèbres de Hopf BT - Séminaire Bourbaki : volume 2000/2001, exposés 880-893 AU - Collectif T3 - Astérisque N1 - talk:892 PY - 2002 DA - 2002/// IS - 282 PB - Société mathématique de France UR - http://archive.numdam.org/item/SB_2000-2001__43__345_0/ UR - https://zbmath.org/?q=an%3A1035.58007 UR - https://www.ams.org/mathscinet-getitem?mr=1975185 LA - fr ID - SB_2000-2001__43__345_0 ER -
Skandalis, Georges. Géométrie non commutative, opérateur de signature transverse et algèbres de Hopf, dans Séminaire Bourbaki : volume 2000/2001, exposés 880-893, Astérisque, no. 282 (2002), Exposé no. 892, 20 p. http://archive.numdam.org/item/SB_2000-2001__43__345_0/
[1] Global theory of elliptic operators, Proc. Int. Conf. Functional Analysis and related topics. Univ. Tokyo Press (1970), 21-30. | MR 266247 | Zbl 0193.43601
-[2] Unitaires multiplicatifs et dualité pour les produits croisés de -algèbres, Ann. Sci. Éc. Norm. Sup. 4e série 26 (1993), 425-488. | Numdam | MR 1235438 | Zbl 0804.46078
& -[3] Transformations pentagonales, C. R. Acad. Sci. Paris Sér. I Math. 327, no. 7 (1998), 623-628. | MR 1652717 | Zbl 1040.37500
& -[4]
& - En préparation.[5] Calculus on Heisenberg manifolds, Annals of Mathematics Studies 119, Princeton University Press, Princeton, NJ (1988). | MR 953082 | Zbl 0654.58033
& -[6] Extensions of -algebras and -homology, Ann. of Math. 105 (1977), 265-324. | MR 458196 | Zbl 0376.46036
, & -[7] Homologie cyclique : rapport sur des travaux récents de Connes, Karoubi, Loday, Quillen..., Sém. Bourbaki, 1983/84, Astérisque 121-122, Soc. Math. France (1985), 123-146. | Numdam | MR 768957 | Zbl 0556.18006
-[8] Spectral geometry of singular Riemannian spaces, J. Differential Geom. 18, no. 4 (1983), 575-657. | MR 730920 | Zbl 0529.58034
-[9] Sur la théorie non commutative de l'intégration, Lect. Notes in Math. 725 (1979), 19-143. | MR 548112 | Zbl 0412.46053
-[10] Noncommutative differential geometry. Chapter I : The Chern character in -homology. Chapter II : De Rham homology and non commutative algebra, Publ. Math. Inst. Hautes Études Sci. 62 (1985), 41-144. | Numdam | MR 823176 | Zbl 0592.46056
-[11] Cyclic cohomology and the transverse fundamental class of a foliation, Geometric methods in operator algebras (Kyoto, 1983), Longman Sci. Tech., Harlow, Pitman Res. Notes Math. Ser. 123 (1986), 52-144. | MR 866491 | Zbl 0647.46054
-[12] Entire cyclic cohomology of Banach algebras and characters of -summable Fredholm modules, -Theory 1, no. 6 (1988), 519-548. | Zbl 0657.46049
-[13] Non commutative geometry, Academic Press, Inc., San Diego, CA (1994).
-[14] Geometry from the spectral point of view, Letters in Mathematical Physics 34 (1995), 203-238. | MR 1345552 | Zbl 1042.46515
-[15] Trace formula in noncommutative geometry and the zeros of the Riemann zeta function, Selecta Math. (N.S.) 5, no. 1 (1999), 29-106. | MR 1694895 | Zbl 0945.11015
-[16] Hopf algebras, renormalization and noncommutative geometry, Comm. Math. Phys. 199, no. 1 (1998), 203-242. | MR 1660199 | Zbl 0932.16038
& -[17] Renormalization in quantum field theory and the Riemann-Hilbert problem I : The Hopf algebra structure of graphs and the main theorem, Comm. Math. Phys. 210, no. 1 (2000), 249-273. | MR 1748177 | Zbl 1032.81026
& -[18] Renormalization in quantum field theory and the Riemann-Hilbert problem. II : The -function, diffeomorphisms and the renormalization group, Comm. Math. Phys. 216, no. 1 (2001), 215-241. | Zbl 1042.81059
& -[19] The local index formula in noncommutative geometry, Geom. Funct. Anal 5, no. 2 (1995), 174-243. | MR 1334867 | Zbl 0960.46048
& -[20] Hopf algebras, cyclic cohomology and the transverse index theorem, Comm. Math. Phys. 198, no. 1 (1998), 199-246. | MR 1657389 | Zbl 0940.58005
& -[21] Cyclic cohomology and Hopf algebras, Letters in Mathematical Physics 48 (1999), 97-108. | MR 1718047 | Zbl 0941.16024
& -[22] Cyclic Cohomology and Hopf Algebra Symmetry, Letters in Mathematical Physics 52 (2000), 1-28. | MR 1800488 | Zbl 0974.58006
& -[23] Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry (preprint 2001). | MR 1929328
& -[24] Cyclic Cohomology of Hopf algebras and a Noncommutative Chern-Weil Theory (preprint 1998). | MR 1868538
-[25] Cohomologies of the Lie algebra of formal vector fields (Russian), Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970), 322-337. | MR 266195 | Zbl 0216.20302
& -[26] Cohomologies d'algèbres de Lie de champs de vecteurs formels, Sém. Bourbaki, 1971/72, exp. no. 421, Lect. Notes in Math. 383 (1974), 69-87. | Numdam | MR 418112 | Zbl 0296.17010
-[27] Elements of noncommutative geometry, Birkhäuser Advanced Texts : Basler Lehrbücher, Boston, MA (2001). | MR 1789831 | Zbl 0958.46039
, & -[28] Morphismes -orientés d'espaces de feuilles et fonctorialité en théorie de Kasparov, Ann. Sci. Éc. Norm. Sup. 4e série 20 (1987), 325-390. | Numdam | MR 925720 | Zbl 0656.57015
& -[29] Quantum -theory. I. The Chern character, Comm. Math. Phys. 118, no. 1 (1988), 1-14. | MR 954672 | Zbl 0656.58048
, & -[30] Extensions of groups to ring groups, Math U.S.S.R. Sbornik 5 (1968), 451-474. | Zbl 0205.03301
-[31] The operator -functor and extensions of -algebras, Math. USSR Izv. 16 (1981), no. 3, 513-572. Translated from : Izv. Akad. Nauk. S.S.S.R. Ser. Mat. 44 (1980), 571-636. | MR 582160 | Zbl 0464.46054
-[32] Le résidu non commutatif (d'après M. Wodzicki), Sém. Bourbaki, vol. 1988/89, exp. no. 708, Astérisque 177-178 (1989), 199-229. | Numdam | MR 1040574 | Zbl 0701.58054
-[33] On the Hopf algebra structure of perturbative quantum field theories, Adv. Theor. Math. Phys. 2, no. 2 (1998), 303-334. | MR 1633004 | Zbl 1041.81087
-[34] Locally compact quantum groups, Ann. Sci. Éc. Norm. Sup. 4e série 33 (6) (2000), 837-934. | Numdam | MR 1832993 | Zbl 1034.46508
& -[35] Triplets spectraux pour les pseudovariétés à singularité conique isolée, C. R. Acad. Sci. Paris Sér. I Math. 327, no. 10 (1998), 871-874. | MR 1663493 | Zbl 0936.46053
-[36] Triplets spectraux pour les pseudo-variétés avec singularité conique isolée. Thèse (preprint 1997).
-[37] Hopf-von Neumann algebra bicrossproducts, Kac algebra bicrossproducts, and the classical Yang-Baxter equations, J.F.A. 95, no. 2 (1991), 291-319. | MR 1092128 | Zbl 0741.46033
-[38] Calcul hypoelliptique sur les variétés de Heisenberg, résidu non commutatif et géométrie pseudo-hermitienne. Thèse (preprint 2000).
-[39] Complex powers of an elliptic operator. Singular Integrals, Proc. Sympos. Pure Math., Chicago, Ill. (1966), Amer. Math. Soc., Providence, R.I. (1967), 288-307. | MR 237943 | Zbl 0159.15504
-[40] Hopf algebras, Mathematics Lecture Note Series - W. A. Benjamin, Inc., New York (1969). | MR 252485 | Zbl 0194.32901
-[41] Matched pairs of groups and bismashed product of Hopf algebras, Comm. Alg. 9 (1981), 841-882. | MR 611561 | Zbl 0456.16011
-[42] Homology of matrix Lie algebras over rings and the Hochschild homology (en russe), Uspekhi Mat. Nauk 38, no. 2 (230) (1983), 217-218. | MR 695483 | Zbl 0518.17002
-[43] Extensions of locally compact quantum groups and the bicrossed product construction (preprint 2001). | MR 1970242
& -[44] Noncommzutative residue. I. Fundamentals, -theory, arithmetic and geometry (Moscow, 19841986-), Lecture Notes in Math. 1289 (Springer, Berlin) (1987), 320-399. | MR 923140 | Zbl 0649.58033
-