K-théorie et multiplicités dans L 2 (G/Γ) (2002)


Pierrot, François
Mémoires de la Société Mathématique de France, Tome 89 (2002) vi-85 p doi : 10.24033/msmf.402
URL stable : http://www.numdam.org/item?id=MSMF_2002_2_89__1_0

Bibliographie

[1] M.F. Atiyah. Elliptic operators, discrete groups and Von Neumann Algebras. Astérisque 32-32 (1976), 43-72. Zbl 0323.58015 | MR 420729

[2] J-B. Bost. Principe d’Oka, K-théorie et systèmes dynamiques non commutatifs. Invent. Math., 101 (1990), 261-333. Zbl 0719.46038 | | MR 1062964

[3] P. Baum & A. Connes. K-theory for Lie groups and foliation, IHES 1982.

[4] P. Baum, A. Connes & N. Higson. Classifying space for proper actions and K-theory of group C * -algebras. In C * -algebras : 1943-1993, vol. 167 of Contemp. Math., 240-291. AMS, RI, 1994. MR 1292018

[5] M. Breuer. Fredholm theories in Von Neumann algebras I, Math. Ann. 178 (1968), 243-254. Zbl 0162.18701 | | MR 234294

[6] A. Connes. Cyclic cohomology and the transverse fundamental class of a foliation. Geometric methods in operator algebras (Kyoto 1983), 52-114, Pitman Res. Notes in Math, 123, 1986. Zbl 0647.46054 | MR 866491

[7] A. Connes & H. Moscovici. The L 2 -index theorem for homogeneous spaces of Lie groups, Ann. of Math. 115 (1982), 291-330. Zbl 0515.58031 | MR 647808

[8] J. Dixmier. Les C * -algèbres et leurs représentations, Gauthier-Villars, 1964. Zbl 0152.32902 | MR 171173

[9] J. Dixmier. Les algèbres d’opérateurs dans l’espace hilbertien. Gauthier-Villars, 1969. Zbl 0175.43801

[10] P. Green. Square integrable representations and the dual topology. JFA 35 (1980), 279-294. Zbl 0439.22009 | MR 563556

[11] A. Grothendieck. Réarrangement de fonctions et inégalités de convexité dans les algèbres de Von Neumann munies d’une trace. Séminaire Bourbaki, mars 1955. Numdam | Zbl 0161.33603 |

[12] N. Higson. The Baum-Connes conjecture, Proc. ICM, Vol. II (Berlin, 1998), Doc. Math., (1998), 637-646. Zbl 0911.46041 | | MR 1648112

[13] N. Higson & G. Kasparov. Operator K-theory for groups which act properly and isometrically on Hilbert space. Electron. Res. Announc. AMS, 3 :131-142 (electronic),1997. Zbl 0888.46046 | | MR 1487204

[14] R. Hotta & R. Parthasarathy. A geometric meaning of the multiplicity of integrable discrete classes in L 2 (G/Γ). Osaka J. Math, 10 (1973), 211-234. Zbl 0337.22016 | MR 338265

[15] R. Hotta & R. Parthasarathy. Multiplicity formulae for discrete series. Invent. Math. 26 (1974), 133-178. Zbl 0298.22013 | | MR 348041

[16] Harish-Chandra. Discrete series for semisimple Lie groups : II, Acta Math. 116 (1966), 1-111. MR 219666

[17] G. Kasparov. Equivariant 𝐾𝐾-theory and the Novikov conjecture, Invent. Math. 91 (1988), 147-201. Zbl 0647.46053 | | MR 918241

[18] V. Lafforgue. Thèse de doctorat. Université Paris Sud, 1999.

[19] V. Lafforgue. Une démonstration de la conjecture de Baum-Connes pour les groupes réductifs sur un corps p-adique et pour certains groupes discrets possédant la propriété (T). CRAS 327 (1998), 439-444. MR 1652538

[20] R.P. Langlands. Dimension of automorphic forms. PSPM vol. 9, 1966, 253-257. Zbl 0215.11802 | MR 212135

[21] P. Muhly, J. Renault & D. Williams. Equivalence and isomorphism for groupoid C * -algebras. J.O.T. 17 (1987), 3-22. Zbl 0645.46040 | MR 873460

[22] C.C. Moore & J.A. Wolf. Square integrable representations of nilpotent Lie groups. Trans. AMS. 185 (1973), 445-462. Zbl 0274.22016 | MR 338267

[23] G. Pedersen. C * -algebras and their automorphism groups. London Math. Soc. monographs vol. 14. Academic Press, 1979. Zbl 0416.46043 | MR 548006

[24] M.A. Rieffel. Morita equivalence for C * -algebras and W * -algebras. J. Pure Appl. Algebra 5 (1974), 51-96. Zbl 0295.46099 | MR 367670

[25] G. Skandalis. Cours de 3e cycle. Paris VII.

[26] E. H. Spanier. Algebraic topology. Mc Graw Hill (1966). Zbl 0145.43303 | MR 210112

[27] R. G. Swan. Topological examples of projective modules. Trans. AMS 230 (1977), 201-234. Zbl 0443.13005 | MR 448350

[28] J.L. Tu. Thèse de doctorat. Université Paris 7, 1996.

[29] A. Valette. K-theory for the reduced C * -algebra of semisimple Lie groups with real rank 1 and finite center. Quart. J. Math. Oxford (2) 35 (1984), 341-359. Zbl 0545.22006 | MR 755672

[30] A. Valette. Minimal projections, integrable representations and property (T). Arch. Math. (Basel) 43 (1984), 397-406. Zbl 0538.22006 | MR 773186

[31] A. Wassermann. Une démonstration de la conjecture de Connes-Kasparov pour les groupes de Lie linéaires connexes réductifs. CRAS 304 (1987), 559-562. Zbl 0615.22011 | MR 894996

[32] F. Williams. Discrete series multiplicities in L 2 (G/Γ). Amer J. Math 106 (1984), 137-148 et 107 (1985), 367-376. MR 729757