Search and download archives of mathematical journals

  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 | 22 citations in Numdam

stable URL:


[I] W. ARVESON, The harmonic analysis of automorphism groups, Operator algebras and applications, Proc. Symposia Pure Math. 38 (I982), part I, I99-269.  MR 84m:46085 |  Zbl 0506.46047
[2] M. F. ATIYAH, Transversally elliptic operators and compact groups, Lecture Notes in Math. 401, Berlin-New York, Springer (I974).  MR 58 #2910 |  Zbl 0297.58009
[3] M. F. ATIYAH, Global theory of elliptic operators, Proc. Internat. Conf. on functional analysis and related topics, Tokyo, Univ. of Tokyo Press (I970), 2I-29.  Zbl 0193.43601
[4] M. F. ATIYAH, K-theory, Benjamin (I967).  Zbl 0159.53302
[5] M. F. ATIYAH and I. SINGER, The index of elliptic operators IV, Ann. of Math. 93 (I97I), II9-I38.  Zbl 0212.28603
[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 (I983), 875-878.  MR 84m:46091 |  Zbl 0551.46041
[7] P. BAUM and A. CONNES, Geometric K-theory for Lie groups and Foliations, Preprint I.H.E.S., I982.  Zbl 0985.46042
[8] P. BAUM and A. CONNES, Leafwise homotopy equivalence and rational Pontrjagin classes, Preprint I.H.E.S., I983.  Zbl 0641.57008
[9] P. BAUM and R. DOUGLAS, K-homology and index theory, Operator algebras and applications, Proc. Symposia Pure Math. 38 (I982), part I, II7-I73.  MR 84d:58075 |  Zbl 0532.55004
[I0] O. BRATTELI, Inductive limits of finite dimensional C*-algebras, Trans. Am. Math. Soc. 171 (I972), I95-234.  MR 47 #844 |  Zbl 0264.46057
[II] L. G. BROWN, R. DOUGLAS and P. A. FILLMORE, Extensions of C*-algebras and K-homology, Ann. of Math. (2) 105 (I977), 265-324.  MR 56 #16399 |  Zbl 0376.46036
[I2] R. CAREY and J. D. PINCUS, Almost commuting algebras, K-theory and operator algebras, Lecture Notes in Math. 575, Berlin-New York, Springer (I977).  MR 58 #23652 |  Zbl 0358.46031
[I3] H. CARTAN and S. EILENBERG, Homological algebra, Princeton University Press (I956).  Zbl 0075.24305
[I4] A. CONNES, The von Neumann algebra of a foliation, Lecture Notes in Physics 80 (I978), I45-I5I, Berlin-New York, Springer.  MR 80i:46057 |  Zbl 0433.46056
[I5] A. CONNES, Sur la théorie non commutative de l'intégration, Algèbres d'opérateurs, Lecture Notes in Math. 725, Berlin-New York, Springer (I979).  MR 81g:46090 |  Zbl 0412.46053
[I6] A. CONNES, A Survey of foliations and operator algebras, Operator algebras and applications, Proc. Symposia Pure Math. 38 (I982), Part I, 52I-628.  MR 84m:58140 |  Zbl 0531.57023
[I7] A. CONNES, Classification des facteurs, Operator algebras and applications, Proc. Symposia Pure Math. 38 (I982), Part II, 43-I09.  MR 84e:46068 |  Zbl 0503.46043
[I8] A. CONNES and G. SKANDALIS, The longitudinal index theorem for foliations, Publ. R.I.M.S., Kyoto, 20 (I984), II39-II83.
Article |  MR 87h:58209 |  Zbl 0575.58030
[I9] A. CONNES, C* algèbres et géométrie différentielle, C.r. Acad. Sci. Paris, Série I, 290 (I980), 599-604.  MR 81c:46053 |  Zbl 0433.46057
[20] A CONNES, Cyclic cohomology and the transverse fundamental class of a foliation, Preprint I.H.E.S. M/84/7 (I984).
[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-I98I.
[22] J. CUNTZ and W. KRIEGER, A class of C*-algebras and topological Markov chains, Invent. Math. 56 (I980), 25I-268.  MR 82f:46073a |  Zbl 0434.46045
[23] J. CUNTZ, K-theoretic amenability for discrete groups, J. Reine Angew. Math. 344 (I983), I80-I95.  MR 86e:46064 |  Zbl 0511.46066
[24] R. DOUGLAS, C*-algebra extensions and K-homology, Annals of Math. Studies 95, Princeton University Press, I980.  MR 82c:46082 |  Zbl 0458.46049
[25] R. DOUGLAS and D. VOICULESCU, On the smoothness of sphere extensions, J. Operator Theory 6 (I) (I98I), I03.  MR 83h:46080 |  Zbl 0501.46055
[26] E. G. EFFROS, D. E HANDELMAN and C. L. SHEN, Dimension groups and their affine representations, Amer. J. Math. 102 (I980), 385-407.  MR 83g:46061 |  Zbl 0457.46047
[27] G. ELLIOTT, On the classification of inductive limits of sequences of semi-simple finite dimensional algebras, J. Alg. 38 (I976), 29-44.  MR 53 #1279 |  Zbl 0323.46063
[28] E. GETZLER, Pseudodifferential operators on supermanifolds and the Atiyah Singer index theorem, Commun. Math. Physics 92 (I983), I63-I78.
Article |  MR 86a:58104 |  Zbl 0543.58026
[29] A. GROTHENDIECK, Produits tensoriels topologiques, Memoirs Am. Math. Soc. 16 (I955).  Zbl 0123.30301
[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 (I973).  MR 52 #11652 |  Zbl 0268.47054
[3I] J. HELTON and R. HOWE, Traces of commutators of integral operators, Acta Math. 135 (I975), 27I-305.  MR 55 #11106 |  Zbl 0332.47010
[32] M. HERMAN, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. Math. I.H.E.S. 49 (I979).
Numdam |  Zbl 0448.58019
[33] G. HOCHSCHILD, B. KOSTANT and A. ROSENBERG, Differential forms on regular affine algebras, Trans. Am. Math. Soc. 102 (I962), 383-408.  MR 26 #167 |  Zbl 0102.27701
[34] L. HÖRMANDER, The Weyl calculus of pseudodifferential operators, Comm. Pure Appl. Math. 32 (I979), 359-443.  Zbl 0388.47032
[35] B. JOHNSON, Cohomology in Banach algebras, Memoirs Am. Math. Soc. 127 (I972).  MR 51 #11130 |  Zbl 0256.18014
[36] B. JOHNSON, Introduction to cohomology in Banach algebras, in Algebras in Analysis, Ed. Williamson, New York, Academic Press (I975), 84-99.  MR 54 #5835 |  Zbl 0306.46065
[37] P. JULG and A. VALETTE, K-moyennabilité pour les groupes opérant sur les arbres, C. r. Acad. Sci. Paris, Série I, 296 (I983), 977-980.  MR 86m:46063 |  Zbl 0537.46055
[38] D. S. KAHN, J. KAMINKER and C. SCHOCHET, Generalized homology theories on compact metric spaces, Michigan Math. J. 24 (I977), 203-224.
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 (I982), I9-27.  MR 84f:57013 |  Zbl 0553.18006
[40] M. KAROUBI, K-theory. An introduction, Grundlehren der Math., Bd. 226 (I978), Springer Verlag.  MR 58 #7605 |  Zbl 0382.55002
[4I] M. KAROUBI et O. VILLAMAYOR, K-théorie algébrique et K-théorie topologique I., Math. Scand. 28 (I97I), 265-307.  MR 47 #1915 |  Zbl 0231.18018
[42] G. KASPAROV, K-functor and extensions of C*-algebras, Izv. Akad. Nauk SSSR, Ser. Mat. 44 (I980), 57I-636.  MR 81m:58075 |  Zbl 0448.46051
[43] G. KASPAROV, K-theory, group C*-algebras and higher signatures, Conspectus, Chernogolovka (I983).
[44] G. KASPAROV, Lorentz groups : K-theory of unitary representations and crossed products, preprint, Chernogolovka, I983.  Zbl 0584.22004
[45] B. KOSTANT, Graded manifolds, graded Lie theory and prequantization, Lecture Notes in Math. 570, Berlin-New York, Springer (I975).  MR 58 #28326 |  Zbl 0358.53024
[46] J. L. LODAY and D. QUILLEN, Cyclic homology and the Lie algebra of matrices, C. r. Acad. Sci. Paris, Série I, 296 (I983), 295-297.  MR 85d:17010 |  Zbl 0536.17006
[47] S. MAC LANE, Homology, Berlin-New York, Springer (I975).
[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 (I974), 85-II2.  Zbl 0299.57010
[5I] G. PEDERSEN, C*-algebras and their automorphism groups, New York, Academic Press (I979).
[52] M. PENINGTON, K-theory and C*-algebras of Lie groups and Foliations, D. Phil. thesis, Oxford, Michaelmas, Term., I983.
[53] M. PENINGTON and R. PLYMEN, The Dirac operator and the principal series for complex semi-simple Lie groups, J. Funct. Analysis 53 (I983), 269-286.  MR 85d:22016 |  Zbl 0542.22013
[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 (I980), 93-II8.  MR 82c:46074 |  Zbl 0474.46059
[55] M. PIMSNER and D. VOICULESCU, Imbedding the irrational rotation C* algebra into an AF algebra, J. of operator theory 4 (I980), 20I-2II.  MR 82d:46086 |  Zbl 0525.46031
[56] M. PIMSNER and D. VOICULESCU, K groups of reduced crossed products by free groups, J. operator theory 8 (I) (I982), I3I-I56.  MR 84d:46092 |  Zbl 0533.46045
[57] M. REED and B. SIMON, Fourier Analysis, Self adjointness, New York, Academic Press (I975).
[58] M. RIEFFEL, C*-algebras associated with irrational rotations, Pac. J. of Math. 95 (2) (I98I), 4I5-429.
Article |  Zbl 0499.46039
[59] J. ROSENBERG, C*-algebras, positive scalar curvature and the Novikov conjecture, Publ. Math. I.H.E.S. 58 (I984), 409-424.
Numdam |  Zbl 0526.53044
[60] W. RUDIN, Real and complex analysis, New York, McGraw Hill (I966).  Zbl 0142.01701
[6I] I. SEGAL, Quantized differential forms, Topology 7 (I968), I47-I72.  MR 38 #1113 |  Zbl 0162.40602
[62] I. SEGAL, Quantization of the de Rham complex, Global Analysis, Proc. Symp. Pure Math. 16 (I970), 205-2I0.  MR 42 #1157 |  Zbl 0214.49001
[63] B. SIMON, Trace ideals and their applications, London Math. Soc. Lecture Notes 35, Cambridge Univ. Press (I979).  MR 80k:47048 |  Zbl 0423.47001
[64] I. M. SINGER, Some remarks on operator theory and index theory, Lecture Notes in Math. 575 (I977), I28-I38, New York, Springer.  MR 57 #7699 |  Zbl 0444.47040
[65] J. L. TAYLOR, Topological invariants of the maximal ideal space of a Banach algebra, Advances in Math. 19 (I976), I49-206.  Zbl 0323.46058
[66] A. M. TORPE, K-theory for the leaf space of foliations by Reeb components, J. Funct. Analysis 61 (I985), I5-7I.  MR 86h:46102 |  Zbl 0594.46062
[67] B. L. TSIGAN, Homology of matrix Lie algebras over rings and Hochschild homology, Uspekhi Math. Nauk. 38 (I983), 2I7-2I8.
[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 (I984), 334-359.  Zbl 0545.22006
[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 (I976).  MR 58 #27769a |  Zbl 0318.33004
[7I] R. WOOD, Banach algebras and Bott periodicity, Topology 4 (I965-I966), 37I-389.  MR 32 #3062 |  Zbl 0163.36702
Copyright Cellule MathDoc 2016 | Credit | Site Map