Morphismes K-orientés d’espaces de feuilles et fonctorialité en théorie de Kasparov (d’après une conjecture d’A. Connes)
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 20 (1987) no. 3, p. 325-390
@article{ASENS_1987_4_20_3_325_0,
     author = {Hilsum, Michel and Skandalis, Georges},
     title = {Morphismes $K$-orient\'es d'espaces de feuilles et fonctorialit\'e en th\'eorie de Kasparov (d'apr\`es une conjecture d'A. Connes)},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Elsevier},
     volume = {4e s{\'e}rie, 20},
     number = {3},
     year = {1987},
     pages = {325-390},
     doi = {10.24033/asens.1537},
     zbl = {0656.57015},
     mrnumber = {90a:58169},
     language = {fr},
     url = {http://www.numdam.org/item/ASENS_1987_4_20_3_325_0}
}
Hilsum, Michel; Skandalis, Georges. Morphismes $K$-orientés d’espaces de feuilles et fonctorialité en théorie de Kasparov (d’après une conjecture d’A. Connes). Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 20 (1987) no. 3, pp. 325-390. doi : 10.24033/asens.1537. http://www.numdam.org/item/ASENS_1987_4_20_3_325_0/

[1] M. F. Atiyah, Elliptic Operators and Compact Groups (Lecture Notes in Math., n° 401, Springer-Verlag, 1974). | MR 482866 | MR 58 #2910 | Zbl 0297.58009

[2] M. F. Atiyah, R. Bott et A. Shapiro, Clifford Modules (Topology, vol. 3, 1964, p. 3-38). | MR 167985 | MR 29 #5250 | Zbl 0146.19001

[3] M. F. Atiyah et I. M. Singer, The Index of Elliptic Operators, I et III, (Annals of Math., vol. 87, 1968, p. 484-530 et p. 546-604, IV, Annals of Math., vol. 93, 1971, p. 119-138). | MR 236950

[4] P. Baum et A. Connes, Geometric K-Theory for Lie Groups and Foliations Preprint I.H.E.S., 1982.

[5] P. Baum et A. Connes, Leafwise Homotopy Equivalence and Rational Pontrjagin Classes, Preprint, I.H.E.S., 1983. | MR 877325 | Zbl 0641.57008

[6] R. Bott, On Characteristic Classes in the Framework of Gel'fand-Fuchs Cohomology (Astérisque, vol. 32-33, 1976, p. 113-139). | MR 402768 | Zbl 0328.57005

[7] A. Connes, Sur la théorie non commutative de l'intégration (Lecture Notes in Math., n° 725, 1979, p. 19-143). | MR 548112 | MR 81g:46090 | Zbl 0412.46053

[8] A. Connes, A Survey of Foliations and Operator Algebras in Operator Algebras and Applications (Proc. Symp. in Pure Math., A.M.S., vol. 38, part. I, 1982, p. 521-628). | MR 679730 | MR 84m:58140 | Zbl 0531.57023

[9] A. Connes, Non-Commutative Differential Geometry, chapter III (à paraître).

[10] A. Connes, Cyclic Cohomology and the Transverse Fundamental Class of a Foliation in Geometric Methods in Operator Algebras, H. ARAKI and E. G. EFFROS éd., Pitman Research Notes in Math., n° 123, Longman/Wiley, 1986, p. 52-144). | MR 88k:58149 | Zbl 0647.46054

[11] A. Connes et G. Skandalis, The Longitudinal Index Theorem for Foliations (Pub. of R.I.M.S., Kyoto, vol. 20, n° 6, 1984, p. 1139-1183). | MR 87h:58209 | Zbl 0575.58030

[12] J. Cuntz, K-Theoretic Amenability for Discrete Groups (J. Reine ang. Math., vol. 344, 1983, p. 180-195). | MR 86e:46064 | Zbl 0511.46066

[13] J. Cuntz et G. Skandalis, Mapping Cones and Exact Sequences in KK-theory (J. of Operator Theory, vol. 15, 1986, p. 163-180). | MR 88b:46099 | Zbl 0603.46063

[14] J. Dixmier et A. Douady, Champs continus d'espaces hilbertiens et de C*-algèbres (Bull. Soc. Math. Fr., t. 91, 1963, p. 227-284). | Numdam | MR 29 #485 | Zbl 0127.33102

[15] T. Fack et G. Skandalis, Sur les représentations et idéaux de la C*-algèbre d'un feuilletage (J. of Operator Theory, vol. 8, 1983, p. 95-129). | MR 84d:46101 | Zbl 0493.46051

[16] I. M. Gel'Fand et D. Fuchs, The Cohomology of the Lie Algebra of Formal Vector Fields (Izv. Ann. S.S.S.R., vol. 34, 1970, p. 327-342). | Zbl 0216.20302

[17] C. Godbillon et J. Vey, Un invariant des feuilletages de codimension 1 (C. R. Acad. Sci. Paris, t. 273, 1971). | MR 44 #1046 | Zbl 0215.24604

[18] P. Green, Equivariant K-theory and Crossed-product C*-algebras, in Operator Algebras and Applications (Proc. Symp. in Pure Math., A.M.S., vol. 38, part. I, 1982, p. 337-338). | MR 85a:46038 | Zbl 0546.46056

[19] A. Grothendieck, Sur quelques points d'algèbre homologique (Tohôku Math. J., vol. 9, 1957, p. 119-221). | MR 21 #1328 | Zbl 0118.26104

[20] A. Haefliger, Variétés Feuilletées (Ann. Scuola Norm. Sup. Pisa, 16, 1962, p. 367-397). | Numdam | MR 32 #6487 | Zbl 0122.40702

[21] A. Haefliger, Differentiable cohomology, Cours au C.I.M.E., 1976.

[22] A. Haefliger, Groupoïde d'holonomie et classifiants (Astérisque, vol. 116, 1984, p. 70-97). | MR 86c:57026a | Zbl 0562.57012

[23] J. Hayden et R. Plymen, On the Invariants of Serre and Dixmier-Douady, Preprint I.H.E.S., 1983.

[24] M. Hilsum et G. Skandalis, Stabilité des C*-algèbres de feuilletages (Ann. de l'Institut Fourier, Grenoble, vol. 33, fasc. 3, 1983, p. 201-208). | Numdam | MR 85f:58115 | Zbl 0505.46043

[25] L. Hörmander, Fourier Integral Operators, I (Acta Math., 127, 1971, p. 79-183). | MR 52 #9299 | Zbl 0212.46601

[26] L. Hörmander, On the Index of Pseudodifferential Operators, Elliptische Differential Gleischungen Band II, Koll., Berlin, 1969.

[27] L. Hörmander, The analysis of linear partial differential operators, vol. I, II, III, IV, Grundlehren der Math. Wis, Springer Verlag (1983).

[28] P. Julg, K-théorie du produit croisé d'une C*-algèbre par un groupe compact (Thèse de 3e cycle, Université Pierre-et-Marie-Curie, 1982).

[29] M. Karoubi, K-Theory, an Introduction (Grundlehren des Math. Wis., Springer-Verlag, 1978). | MR 58 #7605 | Zbl 0382.55002

[30] G. G. Kasparov, Operator K-Functor and Extensions of C*-algebras (Izv. Akad. Nauk. S.S.S.R., Ser. Math., vol. 44, 1980, p. 571-636). | MR 81m:58075 | Zbl 0448.46051

[31] G. G. Kasparov, K-theory, group C*-algebras and higher signatures, conspectus, part. 1.2, Preprint, Chernogolovka, 1981.

[32] G. G. Kasparov, The Index of Invariant Elliptic Operators, K-Theory and Lie Group Representation (Dokl. Akad. Nauk, S.S.S.R., 1983, p. 533-537). | MR 84g:58100 | Zbl 0526.22007

[33] G. G. Kasparov, Lorentz Groups: K-Theory of Unitary Representations and Crossed Products (Dokl. Akad. Nauk S.S.S.R., vol. 275, 1984, p. 541-545; Soviet Math. Dokl., vol. 29, 1984, p. 256-260). | MR 85k:22015 | Zbl 0584.22004

[34] B. Lawson, Foliations (Bull. of A.M.S., vol. 80, 1974, p. 369-418). | Zbl 0293.57014

[35] P. Mulhy, J. Renault et D. Williams, Equivalence and Isomorphisms of Groupoïd C*-Algebras, Preprint, 1985.

[36] R. S. Palais, Seminar on the Atiyah-Singer Index Theorem (Annals of Math. Studies, vol. 57, Princeton, 1965). | MR 33 #6649 | Zbl 0137.17002

[37] J. Renault, A Groupoïd Approach to C*-Algebras (Lecture Notes in Math., n° 793, Springer-Verlag, 1980). | MR 82h:46075 | Zbl 0433.46049

[38] J. Renault, Représentations des produits croisés d'algèbre de groupôdes, Prépublication Université Pierre-et-Marie-Curie, Paris, 1985.

[39] C. Roger, Méthodes homotopiques et cohomologiques en théorie des feuilletages, Prépublication E.N.S.J.F., Paris.

[40] D. Ruelle et D. Sullivan, Currents, Flows and Diffeomorphisms (Topology, vol. 14, 1975, p. 319-327). | MR 54 #3759 | Zbl 0321.58019

[41] G. Skandalis, Some Remarks on KK-Theory (J. of Funct. Anal., vol. 56, n° 3, 1984, p. 337-347). | MR 86c:46085 | Zbl 0561.46035

[42] G. Skandalis, Exact Sequences for the Kasparov Groups of Graded Algebras (Can. J. Math., vol. 37, n° 2, 1985, p. 193-216). | MR 86d:46072 | Zbl 0603.46064

[43] D. Sullivan, Cycles and the Dynamical Studies of Foliated Manifolds (Invent. Math., vol. 36, 1976, p. 225-255). | MR 55 #6440 | Zbl 0335.57015

[44] H. E. Winkelkemper, The Graph of a Foliation (Ann. Global Anal. and Geom., vol. 1, n° 3, 1983, p. 53-75). | MR 85j:57043 | Zbl 0526.53039

[45] R. J. Zimmer, On the von Neumann Algebra of an Ergodic Group Action (Proc. of the A.M.S., vol. 66, n° 2, 1977, p. 289-293). | MR 57 #592 | Zbl 0367.28013

[46] L. Alvarez-Gaumé, Supersymmetry and the Atiyah-Singer Index Theorem (Comm. Math. Phys., vol. 90, 1983, p. 161-173). | MR 85d:58078 | Zbl 0528.58034

[47] E. Getzler, Pseudodifferential Operators on Supermanifolds and the Atiyah-Singer Index Theorem (Comm. Math. Phys., vol. 92, 1983, p. 163-178). | MR 86a:58104 | Zbl 0543.58026

[48] E. Witten, Supersymmetry and Morse Theory (J. Diff. Geom., vol. 17, 1982, p. 661-692). | MR 84b:58111 | Zbl 0499.53056

[49] G. G. Kasparov, Topological Invariants of Elliptic Operators I: K-homology (Math. U.S.S.R. Izv., vol. 9, 1975, p. 751-792). | MR 58 #7603 | Zbl 0337.58006

[50] H. Widom, Families of Pseudo Differential Operators, in Topics in Functional Analysis I. GOHBERG et H. KAC éd. (Adv. in Math., supp. ser. n° 3, 1978). | MR 81c:58062 | Zbl 0477.58035

[51] H. Widom, A Complete Symbolic Calculus for Pseudodifferential Operators (Bull. Sci. Math., vol. 104, 1980, p. 19-63). | MR 81m:58078 | Zbl 0434.35092

[52] G. Skandalis, Une notion de nucléarité en K-théorie (d'après J. Cuntz), Prépublication, 1986.