2009•Comptes Rendus MathématiqueOpen access

Cartan homotopy formulae and the bivariant Hochschild complex

Abhishek Banerjee

Abstract

The formula L D = [ e D + E D , 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.

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Key concepts: Cyclic homology, Hochschild homology, Mathematics, Noncommutative geometry, Homotopy, Homology (biology), Pure mathematics, Commutative property