The cyclic homology of crossed-product algebras, II

Raphaël Ponge

doi:10.1016/j.crma.2017.04.013

Homological algebra/Functional analysis

The cyclic homology of crossed-product algebras, II
[Homologie cycliques des algèbres produits-croisés, II]

Présenté par : Alain Connes

Raphaël Ponge ¹

¹ Department of Mathematical Sciences, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, South Korea

Comptes Rendus. Mathématique, Volume 355 (2017) no. 6, pp. 623-627.

Résumé
Abstract

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 : 2017-03-05
Accepté le : 2017-04-21
Publié le : 2017-05-10

DOI : 10.1016/j.crma.2017.04.013

Affiliations des auteurs :

Raphaël Ponge ¹

¹ Department of Mathematical Sciences, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, South Korea

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     title = {The cyclic homology of crossed-product algebras, {II}},
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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/

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Cité par Sources :

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

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