On a generalized Connes-Hochschild-Kostant-Rosenberg theorem

Details On a generalized Connes-Hochschild-Kostant-Rosenberg theorem On a generalized Connes-Hochschild-Kostant-Rosenberg theorem

2004-04-19

arxiv.org/abs/math/0404329v2

Advances in Mathematics, vol. 200 no. 2 (2006) 303-335

Mathematics

K-Theory and Homology

35 pages, latex2e, uses xypic. To appear in, Advances in Mathematics

Scientific paper

10.1016/j.aim.2004.11.006

The central result here 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 generalizing some fundamental results of Connes and Hochschild-Kostant-Rosenberg. The Connes-Chern character is also identified here with the twisted Chern character.

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