Brisure de symétrie spontanée et géométrie du point de vue spectral

Connes, Alain

Séminaire Bourbaki : volume 1995/96, exposés 805-819, Astérisque, no. 241 (1997), Talk no. 816, 37 p.

EuDML: 110219 | MR: 1472544 | Zbl: 0942.46044

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Connes, Alain. Brisure de symétrie spontanée et géométrie du point de vue spectral, in Séminaire Bourbaki : volume 1995/96, exposés 805-819, Astérisque, no. 241 (1997), Talk no. 816, 37 p. http://archive.numdam.org/item/SB_1995-1996__38__313_0/

References
Cited by

[At] M. F. Atiyah - $K$ -theory and reality, Quart. J. Math. Oxford (2), 17 (1966), 367-386. | DOI | MR | Zbl

[B-G] R. Beals and P. Greiner - Calculus on Heisenberg manifolds, Annals of Math. Studies 119, Princeton Univ. Press, Princeton, N.J., 1988. | MR | Zbl

[B] T. P. Branson - An anomaly associated with $4$ -dimensional quantum gravity, to appear in C.M.P. | MR | Zbl

[B-O] T. P. Branson and B. Ørsted - Explicit functional determinants in four dimensions, Proc. Amer. Math. Soc. 113 (1991), 669-682. | DOI | MR | Zbl

[B-W] A. R. Bernstein and F. Wattenberg - Non standard measure theory, in Applications of model theory to algebra analysis and probability, Edited by W.A.J. Luxenburg Halt, Rinehart and Winstin (1969). | MR | Zbl

[C-J-G] A. H. Chamseddine, J. Fröhlich and O. Grandjean - The gravitational sector in the Connes-Lott formulation of the Standard model, J. Math. Phys. 36, n° 11 (1995). | DOI | MR | Zbl

[C-C] A. Chamseddine and A. Connes - The spectral action principle, to appear. | DOI | MR | Zbl

[Co] A. Connes - Noncommutative geometry, Academic Press (1994). | MR | Zbl

[Co1] A. Connes - Cyclic cohomology and the transverse fundamental class of a foliation, Geometric methods in operator algebras, (Kyoto, 1983), pp. 52-144, Pitman Res. Notes in Math. 123, Longman, Harlow (1986). | MR | Zbl

[Co2] A. Connes - Noncommutative geometry and reality, Journal of Math. Physics 36, n° 11 (1995). | DOI | MR | Zbl

[Co3] A. Connes - Gravity coupled with matter and the foundation of noncommutative geometry, to appear in C.M.P. | MR | Zbl

[Co-L] A. Connes and J. Lott - Particle models and noncommutative geometry, Nuclear Phys. B. 18B (1990), suppl. 29-47 (1991). | MR | Zbl

[C-M1] A. Connes and H. Moscovici - Cyclic cohomology, the Novikov conjecture and hyperbolic groups, Topology 29 (1990), 345-388. | DOI | MR | Zbl

[C-M2] A. Connes and H. Moscovici - The local index formula in noncommutative geometry, GAFA 5 (1995), 174-243. | EuDML | MR | Zbl

[C-M3] A. Connes and H. Moscovici - Hypoelliptic Dirac operator, diffeomorphisms and the transverse fundamental class.

[Co-S] A. Connes and G. Skandalis - The longitudinal index theorem for foliations, Publ. Res. Inst. Math. Sci. Kyoto 20 (1984), 1139-1183. | DOI | MR | Zbl

[C-S-T] A. Connes, D. Sullivan and N. Teleman - Quasiconformal mappings, operators on Hilbert space, and local formulae for characteristic classes, Topology, Vol. 33, n° 4 (1994), 663-681. | DOI | MR | Zbl

[D-T] T. Damour and J. H. Taylor - Strong field tests of relativistic gravity and binary pulsars, Physical Review D, Vol. 45, n° 6 (1992), 1840-1868. | DOI

[Dx] J. Dixmier - Existence de traces non normales, C.R. Acad. Sci. Paris, Ser. A-B 262 (1966). | MR | Zbl

[D-F-R] S. Doplicher, K. Fredenhagen and J. E. Roberts - Quantum structure of space time at the Planck scale and Quantum fields, to appear in CMP. | MR | Zbl

[F] J. Fröhlich - The noncommutative geometry of two dimensional supersymmetric conformal field theory, Preprint ETH (1994).

[G-F] K. Gawedzki and J. Fröhlich - Conformal Field theory and Geometry of Strings, CRM Proceedings and Lecture Notes, Vol. 7 (1994), 57-97. | DOI | MR | Zbl

[Gh] E. Ghys - L'invariant de Godbillon-Vey, Sém. Bourbaki 1988/89, exposé 706, Astérisque 177-178, S.M.F. (1989), 155-181. | EuDML | Numdam | MR | Zbl

[Gi] P. Gilkey - Invariance theory, the heat equation and the Atiyah-Singer index theorem, Math. Lecture Ser. 11, Publish or Perish, Wilmington, Del., 1984. | MR | Zbl

[G] M. Gromov - Carnot-Caratheodory spaces seen from within, Preprint IHES/ M/94/6. | DOI | MR | Zbl

[G-K-P] H. Grosse, C. Klimcik and P. Presnajder - On finite $4$ -dimensional quantum field theory in noncommutative geometry, CERN Preprint TH/96 - 51 Net Hepth/9602115. | MR | Zbl

[H-S] M. Hilsum, G. Skandalis - Morphismes $K$ -orientés d'espaces de feuilles et fonctorialité en théorie de Kasparov, Ann. Sci. Ecole Norm. Sup. (4) 20 (1987), 325-390. | DOI | EuDML | Numdam | MR | Zbl

[I-K-S] B. Iochum, D. Kastler and T. Schücker - Fuzzy mass relations for the Higgs, J.Math. Phys. 36, n° 11 (1995). | DOI | MR | Zbl

[K-W] W. Kalau and M. Walze - Gravity, noncommutative geometry and the Wodzicki residue, J. of Geom. and Phys. 16 (1995), 327-344. | DOI | MR | Zbl

[K] G. Kasparov - The operator $K$ -functor and extensions of $C^{*}$ -algebras, Izv. Akad. Nauk. SSSR Ser. Mat. 44 (1980), 571-636. | MR | Zbl

[Ka] C. Kassel - Le résidu non commutatif, Sém. Bourbaki 1988/89, exposé 708, Astérisque 177-178, S.M.F. (1989), 199-229. | EuDML | Numdam | MR | Zbl

[Kas] D. Kastler - The Dirac operator and gravitation, Commun. Math. Phys. 166 (1995), 633-643. | DOI | MR | Zbl

[Ki] R. C. Kirby - Stable homeomorphisms and the annulus conjecture, Ann. Math. 89 (1969), 575-582. | DOI | MR | Zbl

[L-M] B. Lawson and M. L. Michelson - Spin Geometry, Princeton 1989. | MR | Zbl

[M] Y. Manin - Quantum groups and noncommutative geometry, Centre Recherche Math. Univ. Montréal (1988). | MR | Zbl

[Mi-S] J. Milnor and D. Stasheff - Characteristic classes, Ann. of Math. Stud. 76 Princeton University Press, Princeton, N.J. (1974). | MR | Zbl

[P] S. Power - Hankel operators on Hilbert space, Res. Notes in Math. 64, Pitman, Boston, Mass. (1982). | MR | Zbl

[Ri1] M. A. Rieffel - Morita equivalence for $C^{*}$ -algebras and $W^{*}$ -algebras, J. Pure Appl. Algebra 5 (1974), 51-96. | DOI | MR | Zbl

[Ri2] M. A. Rieffel - $C^{*}$ -algebras associated with irrational rotations, Pacific J. Math. 93 (1981), 415-429 ; MR 83b:46087. | DOI | MR | Zbl

[R] B. Riemann - Mathematical Werke, Dover, New York (1953). | MR

[St] E. Stein - Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, N.J. (1970). | MR | Zbl

[Ste] J. Stern - Le problème de la mesure, Sém. Bourbaki 1983/84, exposé 632, Astérisque 121-122 (1985), 325-346. | EuDML | Numdam | MR | Zbl

[S1] D. Sullivan - Hyperbolic geometry and homeomorphisms in Geometric Topology, Proceed. Georgia Topology Conf. Athens, Georgia (1977), 543-555. | MR | Zbl

[S2] D. Sullivan - Geometric periodicity and the invariants of manifolds, Lecture Notes in Math. 197, Springer (1971). | MR | Zbl

[Ta] M. Takesaki - Tomita's theory of modular Hilbert algebras and its applications, Lecture Notes in Math. 128, Springer (1970). | MR | Zbl

[W] Weinberg - Gravitation and Cosmology, John Wiley and Sons, New York London (1972).

[Wo] M. Wodzicki - Noncommutative residue, Part I. Fundamentals K-theory, arithmetic and geometry, Lecture Notes in Math., 1289, Springer-Berlin (1987). | MR | Zbl