Comptes Rendus
Homological algebra/Functional analysis
The cyclic homology of crossed-product algebras, II
[Homologie cycliques des algèbres produits-croisés, II]
Comptes Rendus. Mathématique, Volume 355 (2017) no. 6, pp. 623-627.

Dans cette note, on produit des quasi-isomorphismes explicites calculant l'homologie cyclique des algèbres produits-croisés provenant d'actions de groupes sur les variétés. On obtient des liens avec la cohomologie équivariante. On étend aussi les résultats de la première partie au cadre des actions de groupes sur les algèbres localement convexes.

In this note, we produce explicit quasi-isomorphisms computing the cyclic homology of crossed-product algebras associated with group actions on manifolds. We obtain explicit relationships with equivariant cohomology. On the way, we extend the results of the first part to the setting of group actions on locally convex algebras.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.04.013

Raphaël Ponge 1

1 Department of Mathematical Sciences, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, South Korea
@article{CRMATH_2017__355_6_623_0,
     author = {Rapha\"el Ponge},
     title = {The cyclic homology of crossed-product algebras, {II}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {623--627},
     publisher = {Elsevier},
     volume = {355},
     number = {6},
     year = {2017},
     doi = {10.1016/j.crma.2017.04.013},
     language = {en},
}
TY  - JOUR
AU  - Raphaël Ponge
TI  - The cyclic homology of crossed-product algebras, II
JO  - Comptes Rendus. Mathématique
PY  - 2017
SP  - 623
EP  - 627
VL  - 355
IS  - 6
PB  - Elsevier
DO  - 10.1016/j.crma.2017.04.013
LA  - en
ID  - CRMATH_2017__355_6_623_0
ER  - 
%0 Journal Article
%A Raphaël Ponge
%T The cyclic homology of crossed-product algebras, II
%J Comptes Rendus. Mathématique
%D 2017
%P 623-627
%V 355
%N 6
%I Elsevier
%R 10.1016/j.crma.2017.04.013
%G en
%F CRMATH_2017__355_6_623_0
Raphaël Ponge. The cyclic homology of crossed-product algebras, II. Comptes Rendus. Mathématique, Volume 355 (2017) no. 6, pp. 623-627. doi : 10.1016/j.crma.2017.04.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.04.013/

[1] P. Baum; A. Connes Chern character for discrete groups, A Fête of Topology, Academic Press, Boston, 1988, pp. 163-232

[2] R. Bott (Lecture Notes in Math.), Volume vol. 652, Springer, Berlin (1978), pp. 25-61

[3] J. Brodzki; S. Dave; V. Nistor The periodic cyclic homology of crossed products of finite type algebras, Adv. Math., Volume 306 (2017), pp. 494-523

[4] J.L. Brylinski Cyclic homology and equivariant theories, Ann. Inst. Fourier (Grenoble), Volume 37 (1987), pp. 15-28

[5] J.L. Brylinski; V. Nistor Cyclic cohomology of étale groupoids, K-Theory, Volume 8 (1994), pp. 341-365

[6] A. Connes Noncommutative differential geometry, Inst. Hautes Études Sci. Publ. Math., Volume 62 (1985), pp. 257-360

[7] A. Connes (Pitman Research Notes in Mathematics), Volume vol. 123, Longman, Harlow (1986), pp. 52-144

[8] A. Connes Noncommutative Geometry, Academic Press, San Diego, 1994

[9] M. Crainic Cyclic cohomology of étale groupoids: the general case, K-Theory, Volume 17 (1999), pp. 319-362

[10] E. Getzler The equivariant Chern character for noncompact Lie groups, Adv. Math., Volume 109 (1994), pp. 88-107

[11] J.D. Jones; C. Kassel Bivariant cyclic theory, K-Theory, Volume 3 (1989), pp. 339-365

[12] C. Kassel Homologie cyclique, caractère de Chern et lemme de perturbation, J. Reine Angew. Math., Volume 408 (1990), pp. 159-180

[13] R. Ponge The cyclic homology of crossed-product algebras, I, C. R. Acad. Sci. Paris, Ser. I, Volume 355 (2017), pp. 618-622

[14] R. Ponge; H. Wang Noncommutative geometry and conformal geometry. II. Connes–Chern character and the local equivariant index theorem, J. Noncommut. Geom., Volume 10 (2016), pp. 307-378

Cité par Sources :

Research partially supported by grants 2013R1A1A2008802 and 2016R1D1A1B01015971 of National Research Foundation of Korea.

Commentaires - Politique