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.
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@article{CRMATH_2017__355_6_623_0, author = {Ponge, Rapha\"el}, 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}, url = {http://www.numdam.org./articles/10.1016/j.crma.2017.04.013/} }
TY - JOUR AU - Ponge, Raphaël 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 UR - http://www.numdam.org./articles/10.1016/j.crma.2017.04.013/ DO - 10.1016/j.crma.2017.04.013 LA - en ID - CRMATH_2017__355_6_623_0 ER -
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/
[1] Chern character for discrete groups, A Fête of Topology, Academic Press, Boston, 1988, pp. 163-232
[2] (Lecture Notes in Math.), Volume vol. 652, Springer, Berlin (1978), pp. 25-61
[3] The periodic cyclic homology of crossed products of finite type algebras, Adv. Math., Volume 306 (2017), pp. 494-523
[4] Cyclic homology and equivariant theories, Ann. Inst. Fourier (Grenoble), Volume 37 (1987), pp. 15-28
[5] Cyclic cohomology of étale groupoids, K-Theory, Volume 8 (1994), pp. 341-365
[6] Noncommutative differential geometry, Inst. Hautes Études Sci. Publ. Math., Volume 62 (1985), pp. 257-360
[7] (Pitman Research Notes in Mathematics), Volume vol. 123, Longman, Harlow (1986), pp. 52-144
[8] Noncommutative Geometry, Academic Press, San Diego, 1994
[9] Cyclic cohomology of étale groupoids: the general case, K-Theory, Volume 17 (1999), pp. 319-362
[10] The equivariant Chern character for noncompact Lie groups, Adv. Math., Volume 109 (1994), pp. 88-107
[11] Bivariant cyclic theory, K-Theory, Volume 3 (1989), pp. 339-365
[12] Homologie cyclique, caractère de Chern et lemme de perturbation, J. Reine Angew. Math., Volume 408 (1990), pp. 159-180
[13] The cyclic homology of crossed-product algebras, I, C. R. Acad. Sci. Paris, Ser. I, Volume 355 (2017), pp. 618-622
[14] Noncommutative geometry and conformal geometry. II. Connes–Chern character and the local equivariant index theorem, J. Noncommut. Geom., Volume 10 (2016), pp. 307-378
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☆ Research partially supported by grants 2013R1A1A2008802 and 2016R1D1A1B01015971 of National Research Foundation of Korea.