Geodesic
Operator 𝐾-theory for groups which act properly and isometrically on Hilbert space
Higson, Nigel1 ; Kasparov, Gennadi2
1 Department of Mathematics, Pennsylvania State University, University Park, PA 16802
2 Institut de Mathématiques de Luminy, CNRS-Luminy-Case 930, 163 Avenue de Luminy 13288, Marseille Cedex 9, France
Electronic research announcements of the American Mathematical Society, Tome 03 (1997), pp. 131-142

Voir la notice de l'article provenant de la source American Mathematical Society

Let $G$ be a countable discrete group which acts isometrically and metrically properly on an infinite-dimensional Euclidean space. We calculate the $K$-theory groups of the $C^{*}$-algebras $C^{*}_{\max }(G)$ and $C^{*}_{ \smash {\text {red}}}(G)$. Our result is in accordance with the Baum-Connes conjecture.
DOI : 10.1090/S1079-6762-97-00038-3

Higson, Nigel 1 ; Kasparov, Gennadi 2

1 Department of Mathematics, Pennsylvania State University, University Park, PA 16802
2 Institut de Mathématiques de Luminy, CNRS-Luminy-Case 930, 163 Avenue de Luminy 13288, Marseille Cedex 9, France 
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Higson, Nigel; Kasparov, Gennadi. Operator 𝐾-theory for groups which act properly and isometrically on Hilbert space. Electronic research announcements of the American Mathematical Society, Tome 03 (1997), pp. 131-142. doi: 10.1090/S1079-6762-97-00038-3

[1] Atiyah, M. F. Bott periodicity and the index of elliptic operators Quart. J. Math. Oxford Ser. (2) 1968 113 140

[2] Baum, Paul, Connes, Alain, Higson, Nigel Classifying space for proper actions and 𝐾-theory of group 𝐶*-algebras 1994 240 291

[3] Bekka, M. E. B., Cherix, P.-A., Valette, A. Proper affine isometric actions of amenable groups 1995 1 4

[4] Blackadar, Bruce 𝐾-theory for operator algebras 1986

[5] Connes, A. An analogue of the Thom isomorphism for crossed products of a 𝐶*-algebra by an action of 𝑅 Adv. in Math. 1981 31 55

[6] Connes, Alain, Higson, Nigel Déformations, morphismes asymptotiques et 𝐾-théorie bivariante C. R. Acad. Sci. Paris Sér. I Math. 1990 101 106

[7] Delorme, Patrick 1-cohomologie des représentations unitaires des groupes de Lie semi-simples et résolubles. Produits tensoriels continus de représentations Bull. Soc. Math. France 1977 281 336

[8] Ferry, Steven C., Ranicki, Andrew, Rosenberg, Jonathan A history and survey of the Novikov conjecture 1995 7 66

[9] Operator algebras and applications. Part 1 1982

[10] Gromov, M. Asymptotic invariants of infinite groups 1993 1 295

[11] De La Harpe, Pierre, Valette, Alain La propriété (𝑇) de Kazhdan pour les groupes localement compacts (avec un appendice de Marc Burger) Astérisque 1989 158

[12] Julg, Pierre 𝐾-théorie équivariante et produits croisés C. R. Acad. Sci. Paris Sér. I Math. 1981 629 632

[13] Kasparov, G. G. Equivariant 𝐾𝐾-theory and the Novikov conjecture Invent. Math. 1988 147 201

[14] Mingo, J. A., Phillips, W. J. Equivariant triviality theorems for Hilbert 𝐶*-modules Proc. Amer. Math. Soc. 1984 225 230

[15] Pedersen, Gert K. 𝐶*-algebras and their automorphism groups 1979

[16] Segal, Graeme Equivariant 𝐾-theory Inst. Hautes Études Sci. Publ. Math. 1968 129 151

[17] Wassermann, Simon Exact 𝐶*-algebras and related topics 1994

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