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Table of contents for this issue | Previous article | Next article Connes, Alain Non-commutative differential geometry. Publications Mathématiques de l'IHÉS, 62 (1985), p. 41-144 Full text djvu | pdf | Reviews MR 87i:58162 | Zbl 0592.46056 | 17 citations in Numdam stable URL: http://www.numdam.org/item?id=PMIHES_1985__62__41_0 Bibliography [2] M. F. ATIYAH, Transversally elliptic operators and compact groups, Lecture Notes in Math. 401, Berlin-New York, Springer ( [3] M. F. ATIYAH, Global theory of elliptic operators, Proc. Internat. Conf. on functional analysis and related topics, Tokyo, Univ. of Tokyo Press ( [4] M. F. ATIYAH, K-theory, Benjamin ( [5] M. F. ATIYAH and I. SINGER, The index of elliptic operators IV, Ann. of Math. 93 ( [6] S. BAAJ et P. JULG, Théorie bivariante de Kasparov et opérateurs non bornés dans les C* modules Hilbertiens, C. r. Acad. Sci. Paris, Série I, 296 ( [7] P. BAUM and A. CONNES, Geometric K-theory for Lie groups and Foliations, Preprint I.H.E.S., [8] P. BAUM and A. CONNES, Leafwise homotopy equivalence and rational Pontrjagin classes, Preprint I.H.E.S., [9] P. BAUM and R. DOUGLAS, K-homology and index theory, Operator algebras and applications, Proc. Symposia Pure Math. 38 ( [I0] O. BRATTELI, Inductive limits of finite dimensional C*-algebras, Trans. Am. Math. Soc. 171 ( [II] L. G. BROWN, R. DOUGLAS and P. A. FILLMORE, Extensions of C*-algebras and K-homology, Ann. of Math. (2) 105 ( [I2] R. CAREY and J. D. PINCUS, Almost commuting algebras, K-theory and operator algebras, Lecture Notes in Math. 575, Berlin-New York, Springer ( [I3] H. CARTAN and S. EILENBERG, Homological algebra, Princeton University Press ( [I4] A. CONNES, The von Neumann algebra of a foliation, Lecture Notes in Physics 80 ( [I5] A. CONNES, Sur la théorie non commutative de l'intégration, Algèbres d'opérateurs, Lecture Notes in Math. 725, Berlin-New York, Springer ( [I6] A. CONNES, A Survey of foliations and operator algebras, Operator algebras and applications, Proc. Symposia Pure Math. 38 ( [I7] A. CONNES, Classification des facteurs, Operator algebras and applications, Proc. Symposia Pure Math. 38 ( [I8] A. CONNES and G. SKANDALIS, The longitudinal index theorem for foliations, Publ. R.I.M.S., Kyoto, 20 ( Article | MR 87h:58209 | Zbl 0575.58030 [I9] A. CONNES, C* algèbres et géométrie différentielle, C.r. Acad. Sci. Paris, Série I, 290 ( [20] A CONNES, Cyclic cohomology and the transverse fundamental class of a foliation, Preprint I.H.E.S. M/84/7 ( [2I] A. CONNES, Spectral sequence and homology of currents for operator algebras. Math. Forschungsinstitut Oberwolfach Tagungsbericht 42/8I, Funktionalanalysis und C*-Algebren, 27-9/3-I0- [22] J. CUNTZ and W. KRIEGER, A class of C*-algebras and topological Markov chains, Invent. Math. 56 ( [23] J. CUNTZ, K-theoretic amenability for discrete groups, J. Reine Angew. Math. 344 ( [24] R. DOUGLAS, C*-algebra extensions and K-homology, Annals of Math. Studies 95, Princeton University Press, [25] R. DOUGLAS and D. VOICULESCU, On the smoothness of sphere extensions, J. Operator Theory 6 (I) ( [26] E. G. EFFROS, D. E HANDELMAN and C. L. SHEN, Dimension groups and their affine representations, Amer. J. Math. 102 ( [27] G. ELLIOTT, On the classification of inductive limits of sequences of semi-simple finite dimensional algebras, J. Alg. 38 ( [28] E. GETZLER, Pseudodifferential operators on supermanifolds and the Atiyah Singer index theorem, Commun. Math. Physics 92 ( Article | MR 86a:58104 | Zbl 0543.58026 [29] A. GROTHENDIECK, Produits tensoriels topologiques, Memoirs Am. Math. Soc. 16 ( [30] J. HELTON and R. HOWE, Integral operators, commutators, traces, index and homology, Proc. of Conf. on operator theory, Lecture Notes in Math. 345, Berlin-New York, Springer ( [3I] J. HELTON and R. HOWE, Traces of commutators of integral operators, Acta Math. 135 ( [32] M. HERMAN, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. Math. I.H.E.S. 49 ( Numdam | Zbl 0448.58019 [33] G. HOCHSCHILD, B. KOSTANT and A. ROSENBERG, Differential forms on regular affine algebras, Trans. Am. Math. Soc. 102 ( [34] L. HÖRMANDER, The Weyl calculus of pseudodifferential operators, Comm. Pure Appl. Math. 32 ( [35] B. JOHNSON, Cohomology in Banach algebras, Memoirs Am. Math. Soc. 127 ( [36] B. JOHNSON, Introduction to cohomology in Banach algebras, in Algebras in Analysis, Ed. Williamson, New York, Academic Press ( [37] P. JULG and A. VALETTE, K-moyennabilité pour les groupes opérant sur les arbres, C. r. Acad. Sci. Paris, Série I, 296 ( [38] D. S. KAHN, J. KAMINKER and C. SCHOCHET, Generalized homology theories on compact metric spaces, Michigan Math. J. 24 ( Article | MR 57 #13921 | Zbl 0384.55001 [39] M. KAROUBI, Connexions, courbures et classes caractéristiques en K-théorie algébrique, Canadian Math. Soc. Proc., Vol. 2, part I ( [40] M. KAROUBI, K-theory. An introduction, Grundlehren der Math., Bd. 226 ( [4I] M. KAROUBI et O. VILLAMAYOR, K-théorie algébrique et K-théorie topologique I., Math. Scand. 28 ( [42] G. KASPAROV, K-functor and extensions of C*-algebras, Izv. Akad. Nauk SSSR, Ser. Mat. 44 ( [43] G. KASPAROV, K-theory, group C*-algebras and higher signatures, Conspectus, Chernogolovka ( [44] G. KASPAROV, Lorentz groups : K-theory of unitary representations and crossed products, preprint, Chernogolovka, [45] B. KOSTANT, Graded manifolds, graded Lie theory and prequantization, Lecture Notes in Math. 570, Berlin-New York, Springer ( [46] J. L. LODAY and D. QUILLEN, Cyclic homology and the Lie algebra of matrices, C. r. Acad. Sci. Paris, Série I, 296 ( [47] S. MAC LANE, Homology, Berlin-New York, Springer ( [48] J. MILNOR, Introduction to algebraic K-theory, Annals of Math. Studies, 72, Princeton Univ. Press. MR 50 #2304 | Zbl 0237.18005 [49] J. MILNOR and D. STASHEFF, Characteristic classes, Annals of Math. Studies 76, Princeton Univ. Press. Zbl 0298.57008 [50] A. S. MIŠčENKO, Infinite dimensional representations of discrete groups and higher signatures, Math. USSR Izv. 8 ( [5I] G. PEDERSEN, C*-algebras and their automorphism groups, New York, Academic Press ( [52] M. PENINGTON, K-theory and C*-algebras of Lie groups and Foliations, D. Phil. thesis, Oxford, Michaelmas, Term., [53] M. PENINGTON and R. PLYMEN, The Dirac operator and the principal series for complex semi-simple Lie groups, J. Funct. Analysis 53 ( [54] M. PIMSNER and D. VOICULESCU, Exact sequences for K-groups and Ext groups of certain cross-product C*-algebras, J. of operator theory 4 ( [55] M. PIMSNER and D. VOICULESCU, Imbedding the irrational rotation C* algebra into an AF algebra, J. of operator theory 4 ( [56] M. PIMSNER and D. VOICULESCU, K groups of reduced crossed products by free groups, J. operator theory 8 (I) ( [57] M. REED and B. SIMON, Fourier Analysis, Self adjointness, New York, Academic Press ( [58] M. RIEFFEL, C*-algebras associated with irrational rotations, Pac. J. of Math. 95 (2) ( Article | Zbl 0499.46039 [59] J. ROSENBERG, C*-algebras, positive scalar curvature and the Novikov conjecture, Publ. Math. I.H.E.S. 58 ( Numdam | Zbl 0526.53044 [60] W. RUDIN, Real and complex analysis, New York, McGraw Hill ( [6I] I. SEGAL, Quantized differential forms, Topology 7 ( [62] I. SEGAL, Quantization of the de Rham complex, Global Analysis, Proc. Symp. Pure Math. 16 ( [63] B. SIMON, Trace ideals and their applications, London Math. Soc. Lecture Notes 35, Cambridge Univ. Press ( [64] I. M. SINGER, Some remarks on operator theory and index theory, Lecture Notes in Math. 575 ( [65] J. L. TAYLOR, Topological invariants of the maximal ideal space of a Banach algebra, Advances in Math. 19 ( [66] A. M. TORPE, K-theory for the leaf space of foliations by Reeb components, J. Funct. Analysis 61 ( [67] B. L. TSIGAN, Homology of matrix Lie algebras over rings and Hochschild homology, Uspekhi Math. Nauk. 38 ( [68] A. VALETTE, K-Theory for the reduced C*-algebra of semisimple Lie groups with real rank one, Quarterly J. of Math., Oxford, Série 2, 35 ( [69] A. WASSERMAN, Une démonstration de la conjecture de Connes-Kasparov, to appear in C. r. Acad. Sci. Paris. [70] A. WEIL, Elliptic functions according to Eisenstein and Kronecker, Erg. der Math., vol. 88, Berlin-New York, Springer ( [7I] R. WOOD, Banach algebras and Bott periodicity, Topology 4 ( |
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