Alain Connes

LIST OF PUBLICATIONS


  1. Sur une généralisation de la notion de corps ordonné. C. R. Acad. Sci. Paris Sér. A-B 269 1969 A337-A340.
  2. Ordres faibles et localisation des zéros de polynomes. C. R. Acad. Sci. Paris Sér. A-B 269 1969 A373-A376.
  3. Ordres faibles et localisation de zéros de polynômes. 1969 Séminaire Choquet: 1968/69, Initiation à l'Analyse, Exp. 5 27 pp. Secrétariat mathématique, Paris 12.
  4. Détermination de modèles minimaux en analyse non standard et application. C. R. Acad. Sci. Paris Sér. A-B 271 1970 A969-A971.
  5. Ultrapuissances et applications dans le cadre de l'analyse non standard. 1970 Séminaire Choquet: 1969/70, Initiation à l'Analyse Fasc. 1, Exp. 8, 25 pp. Secrétariat mathématique, Paris
  6. Un nouvel invariant pour les algèbres de von Neumann. C. R. Acad. Sci. Paris Sér. A-B 273 1971 A900-A903.
  7. Un théorème de décomposition d'applications mesurables. Séminaire Choquet, 10e année (1970/71), Initiation à l'analyse, Fasc. 1, Exp. No. 12, 7 pp. Secrétariat Mathématique, Paris, 1971.
  8. Calcul des deux invariants d'Araki et Woods par la théorie de Tomita et Takesaki. C. R. Acad. Sci. Paris Sér. A-B 274 (1972), A175-A177.
  9. États presque périodiques sur une algèbre de von Neumann. C. R. Acad. Sci. Paris Sér. A-B 274 (1972), A1402-A1405.
  10. Groupe modulaire d'une algèbre de von Neumann. C. R. Acad. Sci. Paris Sér. A-B 274 (1972), A1923-A1926.
  11. Une classification des facteurs de type III. C. R. Acad. Sci. Paris Sér. A-B 275 (1972), A523-A525.
  12. Ordres faibles et localisation de zéros de polynômes. Séminaire Delange-Pisot-Poitou (12e année: 1970/71), Théorie des nombres, Exp. No. 18, 11 pp. Secrétariat Mathématique, Paris, 1972.
  13. The group property of the invariant S of von Neumann algebras. Math. Scand. 32 (1973), 187-192 (1974). [with Alfons van Daele]
  14. Une classification des facteurs de type III. Ann. Sci. École Norm. Sup. (4) 6 (1973), 133-252.
  15. Sur le théorème de Radon-Nikodym pour les poids normaux fidèles semi-finis. Bull. Sci. Math. (2) 97 (1973), 253-258 (1974).
  16. Flots des poids sur les facteurs de type III. C. R. Acad. Sci. Paris Sér. A 278 (1974), 945-948. [with Masamichi Takesaki]
  17. Almost periodic states and factors of type III1. J. Functional Analysis 16 (1974), 415-445.
  18. Existence de facteurs infinis asymtotiquement abéliens. C. R. Acad. Sci. Paris Sér. A 279 (1974), 189-191. [with Edward J. Woods]
  19. Caractérisation des espaces vectoriels ordonnés sous-jacents aux algèbres de von Neumann. Ann. Inst. Fourier (Grenoble) 24 (1974), no. 4, x, 121-155 (1975).
  20. A factor not anti-isomorphic to itself. Ann. Math. (2) 101 (1975), 536-554.
  21. On hyperfinite factors of type III0 and Krieger's factors. J. Functional Analysis 18 (1975), 318-327.
  22. Sur la classification des facteurs de type II. C. R. Acad. Sci. Paris Sér. A-B 281 (1975), no. 1, Aii, A13-A15.
  23. Classification of automorphisms of hyperfinite factors of type II1 and $II_\infty$ and application to type III\ factors. Bull. Amer. Math. Soc. 81 (1975), no. 6, 1090-1092.
  24. Outer conjugacy classes of automorphisms of factors. Ann. Sci. École Norm. Sup. (4) 8 (1975), no. 3, 383-419.
  25. On the hierarchy of W. Krieger. Illinois J. Math. 19 (1975), 428-432.
  26. A factor not anti-isomorphic to itself. Bull. London Math. Soc. 7 (1975), 171-174.
  27. Structure theory for Type III factors. Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974), Vol. 2, pp. 87-91. Canad. Math. Congress, Montreal, Que., 1975.
  28. Outer conjugacy of automorphisms of factors. Symposia Mathematica, Vol. XX (Convegno sulle Algebre C* e loro Applicazioni in Fisica Teorica, Convegno sulla Teoria degli Operatori Indice e Teoria K, INDAM, Rome, 1975), pp. 149-159. Academic Press, London, 1976.
  29. Entropy for automorphisms of II1 von Neumann algebras. Acta Math. 134 (1975), no. 3-4, 289-306. [with Erling Størmer]
  30. On the classification of von Neumann algebras and their automorphisms. Symposia Mathematica, Vol. XX (Convegno sulle Algebre C* e loro Applicazioni in Fisica Teorica, Convegno sulla Teoria degli Operatori Indice e Teoria K, INDAM, Rome, 1975), pp. 435-478. Academic Press, London, 1976.
  31. Classification of injective factors. Cases II1,$ $II_\infty,$ $III_\lambda,$ $\lambda \not=1$. Ann. of Math. (2) 104 (1976), no. 1, 73-115.
  32. Measure space automorphisms, the normalizers of their full groups, and approximate finiteness. J. Functional Analysis 24 (1977), no. 4, 336-352. [with Wolfgang Krieger]
  33. The Tomita-Takesaki theory and classification of type-III factors. C*-algebras and their applications to statistical mechanics and quantum field theory (Proc. Internat. School of Physics "Enrico Fermi", Course LX, Varenna, 1973), pp. 29-46. North-Holland, Amsterdam, 1976.
  34. Periodic automorphisms of the hyperfinite factor of type II1. Acta Sci. Math. (Szeged) 39 (1977), no. 1-2, 39-66.
  35. The flow of weights on factors of type III. Tôhoku Math. J. (2) 29 (1977), no. 4, 473-575. [with Masamichi Takesaki]
  36. Errata: "The flow of weights on factors of type III". Tôhoku Math. J. (2) 30 (1978), no. 4, 653-655. [with Masamichi Takesaki]
  37. Homogeneity of the state space of factors of type III1. J. Functional Analysis 28 (1978), no. 2, 187-196. [with Erling Størmer]
  38. On the cohomology of operator algebras. J. Functional Analysis 28 (1978), no. 2, 248-253.
  39. The von Neumann algebra of a foliation. Mathematical problems in theoretical physics (Proc. Internat. Conf., Univ. Rome, Rome, 1977), pp. 145-151, Lecture Notes in Phys., 80, Springer, Berlin-New York, 1978.
  40. The L2-index theorem for homogeneous spaces. Bull. Amer. Math. Soc. (N.S.) 1 (1979), no. 4, 688-690. [with Henri Moscovici]
  41. Sur la théorie non commutative de l'intégration. Algèbres d'opérateurs (Sém., Les Plans-sur-Bex, 1978), pp. 19-143, Lecture Notes in Math., 725, Springer, Berlin, 1979.
  42. On the equivalence between injectivity and semidiscreteness for operator algebras. Algèbres d'opérateurs et leurs applications en physique mathématique (Proc. Colloq., Marseille, 1977), pp. 107-112, Colloq. Internat. CNRS, 274, CNRS, Paris, 1979.
  43. C* algèbres et géométrie différentielle. C. R. Acad. Sci. Paris Sér. A-B 290 (1980), no. 13, A599-A604.
  44. On the spatial theory of von Neumann algebras. J. Funct. Anal. 35 (1980), no. 2, 153-164.
  45. A factor of type II1 with countable fundamental group. J. Operator Theory 4 (1980), no. 1, 151-153.
  46. Property T and asymptotically invariant sequences. Israel J. Math. 37 (1980), no. 3, 209-210. [with B. Weiss]
  47. von Neumann algebras. Proceedings of the International Congress of Mathematicians (Helsinki, 1978), pp. 97-109, Acad. Sci. Fennica, Helsinki, 1980.
  48. A construction of approximately finite-dimensional non-ITPFI factors. Canad. Math. Bull. 23 (1980), no. 2, 227-230. [with Edward J. Woods]
  49. Théorème de l'indice pour les feuilletages. C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), no. 18, 871-876. [with Georges Skandalis]
  50. An analogue of the Thom isomorphism for crossed products of a C*-algebra by an action of ${\bf R}$. Adv. in Math. 39 (1981), no. 1, 31-55.
  51. Feuilletages et algèbres d'opérateurs. Bourbaki Seminar, Vol. 1979/80, pp. 139-155, Lecture Notes in Math., 842, Springer, Berlin-New York, 1981.
  52. An amenable equivalence relation is generated by a single transformation. Ergodic Theory Dynamical Systems 1 (1981), no. 4, 431-450. [with J. Feldman and B. Weiss]
  53. A II1 factor with two nonconjugate Cartan subalgebras. Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 2, 211-212. [with Vaughan Jones]
  54. L2-index theory on homogeneous spaces and discrete series representations. , pp. 419-433, Proc. Sympos. Pure Math., 38, Amer. Math. Soc., Providence, R.I., 1982. [with Henri Moscovici]
  55. Classification des facteurs. Operator algebras and applications, Part 2 (Kingston, Ont., 1980), pp. 43-109, Proc. Sympos. Pure Math., 38, Amer. Math. Soc., Providence, R.I., 1982.
  56. The L2-index theorem for homogeneous spaces of Lie groups. Ann. of Math. (2) 115 (1982), no. 2, 291-330. [with Henri Moscovici]
  57. A survey of foliations and operator algebras. , pp. 521-628, Proc. Sympos. Pure Math., 38, Amer. Math. Soc., Providence, R.I., 1982.
  58. Cohomologie cyclique et foncteurs Extn. C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), no. 23, 953-958.
  59. A connection between the classical and the quantum mechanical entropies. Operator algebras and group representations, Vol. I (Neptun, 1980), 113-123, Monographs Stud. Math., 17, Pitman, Boston, Mass.-London, 1984. [with Erling Størmer]
  60. Caractère multiplicatif d'un module de Fredholm. [Multiplicative character of a Fredholm module] C. R. Acad. Sci. Paris Sér. I Math. 299 (1984), no. 19, 963-968. [with Max Karoubi]
  61. The longitudinal index theorem for foliations. Publ. Res. Inst. Math. Sci. 20 (1984), no. 6, 1139-1183. [with Georges Skandalis]
  62. Property T for von Neumann algebras. Bull. London Math. Soc. 17 (1985), no. 1, 57-62. [with Vaughan Jones]
  63. Approximately transitive flows and ITPFI factors. Ergodic Theory Dynamical Systems 5 (1985), no. 2, 203-236. [with Edward J. Woods]
  64. Entropie de Kolmogoroff-Sinai et mécanique statistique quantique. C. R. Acad. Sci. Paris Sér. I Math. 301 (1985), no. 1, 1-6.
  65. Introduction to noncommutative differential geometry. Workshop Bonn 1984 (Bonn, 1984), 3-16, Lecture Notes in Math., 1111, Springer, Berlin-New York, 1985.
  66. Noncommutative differential geometry. Inst. Hautes Études Sci. Publ. Math. No. 62 (1985), 257-360.
  67. Factors of type III1, property $L_\lambda'$ and closure of inner automorphisms. J. Operator Theory 14 (1985), no. 1, 189-211.
  68. Diameters of state spaces of type III factors. Operator algebras and their connections with topology and ergodic theory (Bu\c steni, 1983), 91-116, Lecture Notes in Math., 1132, Springer, Berlin-New York, 1985. [with Uffe Haagerup and Erling Størmer]
  69. Leafwise homotopy equivalence and rational Pontrjagin classes. Foliations (Tokyo, 1983), 1-14, Adv. Stud. Pure Math., 5, North-Holland, Amsterdam-New York, 1985. [with Paul Baum]
  70. Indice des sous facteurs, algèbres de Hecke et théorie des n\oe uds (d'après Vaughan Jones). Seminar Bourbaki, Vol. 1984/85. Astérisque No. 133-134 (1986), 289-308.
  71. Transgression du caractère de Chern et cohomologie cyclique. C. R. Acad. Sci. Paris Sér. I Math. 303 (1986), no. 18, 913-918. [with Henri Moscovici]
  72. Cyclic cohomology and the transverse fundamental class of a foliation. Geometric methods in operator algebras (Kyoto, 1983), 52-144, Pitman Res. Notes Math. Ser., 123, Longman Sci. Tech., Harlow, 1986.
  73. Yang-Mills for noncommutative two-tori. Operator algebras and mathematical physics (Iowa City, Iowa, 1985), 237-266, Contemp. Math., 62, Amer. Math. Soc., Providence, R.I., 1987. [with Marc A. Rieffel]
  74. Dynamical entropy of C* algebras and von Neumann algebras. Comm. Math. Phys. 112 (1987), no. 4, 691-719. [with H. Narnhofer and W. Thirring]
  75. Cyclic cohomology and noncommutative differential geometry. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), 879-889, Amer. Math. Soc., Providence, RI, 1987.
  76. Quasi homomorphismes, cohomologie cyclique et positivité. Comm. Math. Phys. 114 (1988), no. 3, 515-526. [with J. Cuntz]
  77. Cyclic cohomology and noncommutative differential geometry. Géométrie différentielle (Paris, 1986), 33-50, Travaux en Cours, 33, Hermann, Paris, 1988.
  78. Entire cyclic cohomology of Banach algebras and characters of $\theta$-summable Fredholm modules. K-Theory 1 (1988), no. 6, 519-548.
  79. Caractère multiplicatif d'un module de Fredholm. K-Theory 2 (1988), no. 3, 431-463. [with Max Karoubi]
  80. Trace de Dixmier, modules de Fredholm et géométrie riemannienne. Conformal field theories and related topics (Annecy-le-Vieux, 1988). Nuclear Phys. B Proc. Suppl. 5b (1988), 65-70.
  81. Conjecture de Novikov et groupes hyperboliques. C. R. Acad. Sci. Paris Sér. I Math. 307 (1988), no. 9, 475-480. [with Henri Moscovici]
  82. Chern character for discrete groups. A fête of topology, 163-232, Academic Press, Boston, MA, 1988. [with Paul Baum]
  83. The action functional in noncommutative geometry. Comm. Math. Phys. 117 (1988), no. 4, 673-683.
  84. K-theory for discrete groups. Operator algebras and applications, Vol. 1, 1-20, London Math. Soc. Lecture Note Ser., 135, Cambridge Univ. Press, Cambridge, 1988. [with Paul Baum]
  85. Noncommutative geometry. Nonperturbative quantum field theory (Cargèse, 1987), 33-69, NATO Adv. Sci. Inst. Ser. B: Phys., 185, Plenum, New York, 1988.
  86. Hyperfinite von Neumann algebras and Poisson boundaries of time dependent random walks. Pacific J. Math. 137 (1989), no. 2, 225-243. [with Edward J. Woods]
  87. Compact metric spaces, Fredholm modules, and hyperfiniteness. Ergodic Theory Dynamical Systems 9 (1989), no. 2, 207-220.
  88. Embedding of U(1)-current algebras in noncommutative algebras of classical statistical mechanics. Comm. Math. Phys. 121 (1989), no. 3, 507-525. [with David E. Evans]
  89. Conjecture de Novikov et fibrés presque plats. C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), no. 5, 273-277. [with Mikhaïl Gromov and Henri Moscovici]
  90. Operator algebras, unitary representations, enveloping algebras, and invariant theory. Papers from the colloquium in honor of Jacques Dixmier held at the Institute Henri Poincaré, Paris, May 22-26, 1989. Edited by Alain Connes, Michel Duflo, Anthony Joseph and Rudolf Rentschler. Progress in Mathematics, 92. Birkhäuser Boston, Inc., Boston, MA, 1990. xviii+579 pp.
  91. Déformations, morphismes asymptotiques et K-théorie bivariante. C. R. Acad. Sci. Paris Sér. I Math. 311 (1990), no. 2, 101-106. [with Nigel Higson]
  92. Cyclic cohomology, the Novikov conjecture and hyperbolic groups. Topology 29 (1990), no. 3, 345-388. [with Henri Moscovici]
  93. Caractères des représentations $\theta$-sommables des groupes discrets. C. R. Acad. Sci. Paris Sér. I Math. 312 (1991), no. 9, 661-666.
  94. Géométrie non commutative. InterEditions, Paris, 1990. 240 pp.
  95. Introduction à la géométrie non-commutative. The legacy of John von Neumann (Hempstead, NY, 1988), 91-118, Proc. Sympos. Pure Math., 50, Amer. Math. Soc., Providence, RI, 1990.
  96. Essay on physics and noncommutative geometry. The interface of mathematics and particle physics (Oxford, 1988), 9-48, Inst. Math. Appl. Conf. Ser. New Ser., 24, Oxford Univ. Press, New York, 1990.
  97. Particle models and noncommutative geometry. Recent advances in field theory (Annecy-le-Vieux, 1990). Nuclear Phys. B Proc. Suppl. 18B (1990), 29-47 (1991). [with John Lott]
  98. On the Chern character of $\theta$ summable Fredholm modules. Comm. Math. Phys. 139 (1991), no. 1, 171-181.
  99. Sur la nature de la réalité mathématique. [On the nature of mathematical reality] Elem. Math. 47 (1992), no. 1, 19-26.
  100. Closed star products and cyclic cohomology. Lett. Math. Phys. 24 (1992), no. 1, 1-12. [with Moshé Flato and Daniel Sternheimer]
  101. Produits eulériens et facteurs de type III. C. R. Acad. Sci. Paris Sér. I Math. 315 (1992), no. 3, 279-284. [with Jean-Benoît Bost]
  102. The metric aspect of noncommutative geometry. New symmetry principles in quantum field theory (Cargèse, 1991), 53-93, NATO Adv. Sci. Inst. Ser. B Phys., 295, Plenum, New York, 1992. [with John Lott]
  103. Matière à pensée. Reprint of the 1989 edition. Points. Editions Odile Jacob, Paris, 1992. 268 pp. ISBN: 2-02-014676-2 [with Jean-Pierre Changeux]
  104. Géométrie non commutative et physique quantique. Mathématiques quantiques, 20 pp., SMF Journ. Annu., 1992, Soc. Math. France, Paris, 1992.
  105. Noncommutative geometry. Mathematical research today and tomorrow (Barcelona, 1991), 40-58, Lecture Notes in Math., 1525, Springer, Berlin, 1992.
  106. Group cohomology with Lipschitz control and higher signatures. Geom. Funct. Anal. 3 (1993), no. 1, 1-78. [with Mikhaïl Gromov and Henri Moscovici]
  107. Formules locales pour les classes de Pontrjagin topologiques. C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), no. 5, 521-526. [with Dennis Sullivan and Nicolas Teleman]
  108. Transgression and the Chern character of finite-dimensional K-cycles. Comm. Math. Phys. 155 (1993), no. 1, 103-122. [with Henri Moscovici]
  109. Interprétation géométrique du modèle standard de la physique des particules et structure fine de l'espace-temps. C. R. Acad. Sci. Paris Sér. Gén. Vie Sci. 10 (1993), no. 3, 223-234.
  110. Quasiconformal mappings, operators on Hilbert space, and local formulae for characteristic classes. Topology 33 (1994), no. 4, 663-681. [with Dennis Sullivan and Nicolas Teleman]
  111. von Neumann algebra automorphisms and time-thermodynamics relation in generally covariant quantum theories. Classical Quantum Gravity 11 (1994), no. 12, 2899-2917. [with C. Rovelli]
  112. Noncommutative geometry. Academic Press, Inc., San Diego, CA, 1994. xiv+661 pp.
  113. Classifying space for proper actions and K-theory of group C*-algebras. C*-algebras: 1943-1993 (San Antonio, TX, 1993), 240-291, Contemp. Math., 167, Amer. Math. Soc., Providence, RI, 1994. [with Paul Baum and Nigel Higson]
  114. Conversations on mind, matter, and mathematics. Edited and translated from the 1989 French original by M. B. DeBevoise. Princeton University Press, Princeton, NJ, 1995. xii+261 pp. [with Jean-Pierre Changeux]
  115. The local index formula in noncommutative geometry. Geom. Funct. Anal. 5 (1995), no. 2, 174-243. [with Henri Moscovici]
  116. Noncommutative geometry and reality. J. Math. Phys. 36 (1995), no. 11, 6194-6231.
  117. Geometry from the spectral point of view. Lett. Math. Phys. 34 (1995), no. 3, 203-238.
  118. Quantized calculus and applications. XIth International Congress of Mathematical Physics (Paris, 1994), 15-36, Internat. Press, Cambridge, MA, 1995.
  119. Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory. Selecta Math. (N.S.) 1 (1995), no. 3, 411-457. [with Jean-Benoît Bost]
  120. Polarized modules and Fredholm modules. Mat. Fiz. Anal. Geom. 2 (1995), no. 1, 15-24. [with J. Brodzki and D. Ellwood]
  121. Round table: physics and mathematics. XIth International Congress of Mathematical Physics (Paris, 1994), 691-705, Internat. Press, Cambridge, MA, 1995. [with J. Lebowitz, M. Atiyah, E. Brézin, J. Fröhlich, D. Gross, A. Jaffe, L. Kadanoff, and D. Ruelle]
  122. Formule de trace en géométrie non-commutative et hypothèse de Riemann. C. R. Acad. Sci. Paris Sér. I Math. 323 (1996), no. 12, 1231-1236.
  123. Gravity coupled with matter and the foundation of non-commutative geometry. Comm. Math. Phys. 182 (1996), no. 1, 155-176.
  124. Matrix Vieta theorem revisited. Lett. Math. Phys. 39 (1997), no. 4, 349-353. [with Albert Schwarz]
  125. Aspherical gravitational monopoles. Nuclear Phys. B 490 (1997), no. 1-2, 391-431. [with Thibault Damour and Pierre Fayet]
  126. Non-commutative geometry and physics. Gravitation et quantifications (Les Houches, 1992), 805-950, North-Holland, Amsterdam, 1995.
  127. Universal formula for noncommutative geometry actions: unification of gravity and the standard model. Phys. Rev. Lett. 77 (1996), no. 24, 4868-4871.
  128. The spectral action principle. Comm. Math. Phys. 186 (1997), no. 3, 731-750. [with Ali H. Chamseddine]
  129. Brisure de symétrie spontanée et géométrie du point de vue spectral. Séminaire Bourbaki, Vol. 1995/96. Astérisque No. 241 (1997), Exp. No. 816, 5, 313-349; J. Geom. Phys. 23 (1997), no. 3-4, 206-234; and Fields Medallists' lectures, 340-371, World Sci. Ser. 20th Century Math., 5, World Sci. Publishing, River Edge, NJ, 1997.
  130. Noncommutative differential geometry and the structure of space time. Operator algebras and quantum field theory (Rome, 1996), 330-358, Internat. Press, Cambridge, MA, 1997; Cyclic cohomology and noncommutative geometry (Waterloo, ON, 1995), 17-42, Fields Inst. Commun., 17, Amer. Math. Soc., Providence, RI, 1997; Deformation theory and symplectic geometry (Ascona, 1996), 1-33, Math. Phys. Stud., 20, Kluwer Acad. Publ., Dordrecht, 1997; and Quantum fields and quantum space time (Cargèse, 1996), 45-72, NATO Adv. Sci. Inst. Ser. B Phys., 364, Plenum, New York, 1997.
  131. Trace formula in noncommutative geometry and the zeros of the Riemann zeta function. Journées "Équations aux Dérivées Partielles" (Saint-Jean-de-Monts, 1997), Exp. No. IV, 28 pp., École Polytech., Palaiseau, 1997.
  132. Noncommutative geometry and matrix theory: compactification on tori. J. High Energy Phys. 1998, no. 2, Paper 3, 35 pp. (electronic). [with Michael R. Douglas and Albert Schwarz]
  133. Hopf algebras, cyclic cohomology and the transverse index theory. Preprint. [with Henri Moscovici]
  134. Hopf Algebras, renormalization and noncommutative geometry. Preprint. [with Dirk Kreimer]

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