On a generalised Connes-Hochschild-Kostant-Rosenberg theorem

Abstract

The central result of this paper is an explicit computation of the Hochschild and cyclic homologies of a natural smooth subalgebra of stable continuous trace algebras having smooth manifolds X as their spectrum. More precisely, the Hochschild homology is identified with the space of differential forms on X, and the periodic cyclic homology with the twisted de Rham cohomology of X, thereby generalising some fundamental results of Connes and Hochschild–Kostant–Rosenberg. The Connes–Chern character is also identified here with the twisted Chern character.