Cartan homotopy formulae and the bivariant Hochschild complex

Banerjee, Abhishek

doi:10.1016/j.crma.2009.07.016

Homological Algebra/Lie Algebras

Cartan homotopy formulae and the bivariant Hochschild complex
[Formule homotopique de Cartan et le complexe de Hochschild bivariant]

Présenté par : Alain Connes

Banerjee, Abhishek ¹

¹ Department of Mathematics, Johns Hopkins University, 3400 N Charles St., 404 Krieger Hall, Baltimore, MD 21218, USA

Comptes Rendus. Mathématique, Tome 347 (2009) no. 17-18, pp. 997-1000.

Résumé
Abstract

La formule $L_{D} = [e_{D} + E_{D}, \bar{b} + \bar{B}]$ (voir Goodwillie [Cyclic homology, derivations, and the free loopspace, Topology 24 (2) (1985) 187–215]) sur le complexe de Hochschild normalisé joue le rôle, en géométrie non commutative, de la formule homotopique de Cartan en homologie de Rham. Notre but est détendre cette formule au complexe de Hochschild bivariant normalisée.

The formula $L_{D} = [e_{D} + E_{D}, \bar{b} + \bar{B}]$ (see Goodwillie [Cyclic homology, derivations, and the free loopspace, Topology 24 (2) (1985) 187–215]) on the normalized Hochschild complex is the standard replacement in noncommutative geometry for the classical Cartan homotopy formula. Our purpose is to extend this formula to the normalized bivariant Hochschild complex.

Reçu le : 2009-04-15
Accepté le : 2009-07-17
Publié le : 2009-08-13

DOI : 10.1016/j.crma.2009.07.016

Affiliations des auteurs :

Banerjee, Abhishek ¹

¹ Department of Mathematics, Johns Hopkins University, 3400 N Charles St., 404 Krieger Hall, Baltimore, MD 21218, USA

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Banerjee, Abhishek. Cartan homotopy formulae and the bivariant Hochschild complex. Comptes Rendus. Mathématique, Tome 347 (2009) no. 17-18, pp. 997-1000. doi : 10.1016/j.crma.2009.07.016. http://www.numdam.org/articles/10.1016/j.crma.2009.07.016/

Bibliographie
Cité par

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[3] Goodwillie, T.G. Cyclic homology, derivations, and the free loopspace, Topology, Volume 24 (1985) no. 2, pp. 187-215

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