no. 17-18
Homological Algebra/Lie Algebras
Cartan homotopy formulae and the bivariant Hochschild complex

Presented by: Alain Connes

Banerjee, Abhishek1
1 Department of Mathematics, Johns Hopkins University, 3400 N Charles St., 404 Krieger Hall, Baltimore, MD 21218, USA
Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 997-1000.

The formula LD=[eD+ED,b¯+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.

La formule LD=[eD+ED,b¯+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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.07.016
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, Volume 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/

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