Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M.F. Atiyah, Global theory of elliptic operators, Proc. Internat. Conf. on functional analysis and related topics, Univ. of Tokyo Press, Tokyo (1970).
M.F. Atiyah, K theory, Benjamin (1967).
M.F. Atiyah and I. Singer, The index of elliptic operators IV, Ann. of Math. 93 (1971) p. 119–138.
P. Baum and A. Connes, Geometric K theory for Lie groups and Foliations, Preprint IHES, 1982.
P. Baum and A. Connes, Leafwise homotopy equivalence and rational Pontrjagin classes, Preprint IHES, 1983.
P. Baum and R. Douglas, K homotopy and index theory, Operator algebras and applications, Proc. Symposia Pure Math. 38 (1982), part I, p. 117–173.
O. Bratteli, Inductive limits of finite dimensional C*-algebras, Trans. AMS 171 (1972), p. 195–234.
L.G. Brown, R. Douglas and P.A. Fillmore, Extensions of C*-algebras and K homology, Ann. of Math. (2) 105 (1977) p. 265–324.
R. Carey and J.D. Pincus, Almost commuting algebras, K theory and operator algebras, Lecture Notes in Math. No575, Springer Berlin-New York (1977).
A. Connes, The von Neumann algebra of a foliation, Lecture Notes in Physics No80 (1978) p. 145–151, Springer Berlin-New York.
A. Connes, Sur la théorie non commutative de l’intégration, Algèbres d’opérateurs, Lecture Notes in Math. No725, Springer Berlin-New York (1979).
A. Connes, A Survey of foliations and operator algebras, Operator algebras and applications, Proc. Symposia Pure Math. 38 (1982) Part I, p. 521–628.
A. Connes, Classification des facteurs, Operator algebras and applications, Proc. Symposia Pure Math. 38 (1982) Part II, p. 43–109.
A. Connes and G. Skandalis, The longitudinal index theorem for foliations, to appear in Publ. R.I.M.S. Kyoto.
A. Connes, C*-algèbres et géométrie différentielle, C.R.Acad. Sci. Paris, tome 290, Série I (1980).
A. Connes, Cyclic cohomology and the transverse fundamental class of a foliation, Preprint IHES M/84/7.
A. Connes, Spectral sequence and homology of currents for operator algebras. Math. Forschungsinstitut Oberwolfach Tagungsbericht 42/81, Funktionalanalysis und C*-Algebren, 27.9.–3.10.1981.
J. Cuntz and W. Krieger, A class of C*-algebras and topological Markov chains, Invent. Math. 56 (1980) p. 251–268.
R. Douglas, C*-algebra extensions and K homology, Annals of Math. Studies, No95, Princeton University Press 1980.
R. Douglas and D. Voiculescu, On the smoothness of sphere extensions, J. Operator Theory 6(1) (1981) p. 103.
E.G. Effros, D.E. Handelman and C.L. Shen, Dimension groups and their affine representations, Amer. J. Math. 102 (1980), p. 385–407.
G. Elliott, On the classification of inductive limits of sequences of semi-simple finite dimensional algebras, J. Alg. 38 (1976) p. 29–44.
J. Helton and R. Howe, Integral operators, commutators, traces, index and homology, Proc. of Conf. on operator theory, Lecture Notes in Math. No345, Springer Berlin-New York (1973).
D.S. Kahn, J. Kaminker and C. Schochet, Generalized homology theories on compact metric spaces, Michigan Math. J. 24 (1977) p. 203–224.
M. Karoubi, Connexions, courbures et classes caractéristiques en K theorie algébrique, Canadian Math. Soc. Proc. Vol.2, part I (1982) p. 19–27.
G. Kasparov, K functor and extensions of C*-algebras, Izv. Akad. Nauk SSSR, Ser. Mat. 44 (1980) p. 571–636.
G. Kasparov, K theory, group C*-algebras and higher signature, Conspectus, Chernogolovka (1983).
G. Kasparov, Lorentz groups: K theory of unitary representations and crossed products, preprint, Chernogolovka, 1983.
J.L. Loday and D. Quillen, Cyclic homology and the Lie algebra of matrices, C.R. Acad. Sci. Paris, Série I, 296 (1983) p. 295–297.
A.S. Miscenko, Infinite dimensional representations of discrete groups and higher signature, Math. USSR Izv. 8 (1974) p. 85–112.
M. Penington, K theory and C*-algebras of Lie groups and Foliations, D. Phil. thesis, Michaelmas, Term. 1983, Oxford.
M. Penington and R. Plymen, The Dirac operator and the principal series for complex semi-simple Lie groups, J. Funct. Analysis 53 (1983) p. 269–286.
G. Pedersen, C*-algebras and their automorphism groups. Academic Press, New York (1979).
M. Pimsner and D. Voiculescu, Exact sequences for K groups and Ext groups of certain cross-product C*-algebras. J. of operator theory 4 (1980), 93–118.
M. Pimsner and D. Voiculescu, Imbedding the irrational rotation C* algebra into an AF algebra, J. of operator theory 4 (1980) 201–211.
M. Rieffel, C*-algebras associated with irrational rotations, Pac. J. of Math. 93, No2 (1981).
J. Rosenberg, C* algebras, positive scalar curvature and the Novikov conjecture, Publ. Math. IHES, Vol. 58 (1984), p. 409–424.
W. Rudin, Real and complex analysis, Mc. Graw Hill, New York (1966).
I. Segal, Quantized differential forms, Topology 7 (1968) p. 147–172.
I.M. Singer, Some remarks on operator theory and index theory, Lecture notes in Math. 575 (1977) p. 128–138, Springer New York.
J.L. Taylor, Topological invariants of the maximal ideal space of a Banach algebra, Advances in Math. 19 (1976) No2, p. 149–206.
B.L. Tsigan, Homology of matrix Lie algebras over rings and Hochschild homology, Uspekhi Math. Nauk. Vol. 38 (1983) p. 217–218.
A.M. Torpe, K theory for the leaf space of foliations by Reeb components, Mat. Institut, Odense Univ., Preprint (1982).
A. Valette, K. Theory for the reduced C*-algebra of semisimple Lie groups with real rank one, Quarterly J. of Math., Oxford Série 2, Vol. 35 (1984) p. 334–359.
A. Wasserman, Une démonstration de la conjecture de Connes-Kasparov, To appear in C.R. Acad. Sci. Paris.
R. Wood, Banach algebras and Bott periodicity, Topology 4 (1965–66) p. 371–389.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1985 Springer-Verlag
About this paper
Cite this paper
Connes, A. (1985). Introduction to non commutative differential geometry. In: Hirzebruch, F., Schwermer, J., Suter, S. (eds) Arbeitstagung Bonn 1984. Lecture Notes in Mathematics, vol 1111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084582
Download citation
DOI: https://doi.org/10.1007/BFb0084582
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15195-1
Online ISBN: 978-3-540-39298-9
eBook Packages: Springer Book Archive