no. 6
Homological algebra/Functional analysis
The cyclic homology of crossed-product algebras, II
[Homologie cycliques des algèbres produits-croisés, II]

Présenté par : Alain Connes

Ponge, Raphaël1
1 Department of Mathematical Sciences, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, South Korea
Comptes Rendus. Mathématique, Tome 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
Ponge, Raphaël 1

1 Department of Mathematical Sciences, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, South Korea 
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Ponge, Raphaël. The cyclic homology of crossed-product algebras, II. Comptes Rendus. Mathématique, Tome 355 (2017) no. 6, pp. 623-627. doi : 10.1016/j.crma.2017.04.013. http://www.numdam.org/articles/10.1016/j.crma.2017.04.013/

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