Secondary Invariants for Frechet Algebras, Quasihomomorphisms, and the Residue Chern Character
نویسنده
چکیده
A Fréchet algebra endowed with a multiplicatively convex topology has two types of invariants: homotopy invariants (topological K-theory and periodic cyclic homology) and secondary invariants (multiplicative Ktheory and the non-periodic versions of cyclic homology). The first aim of this paper is to establish a Riemann-Roch-Grothendieck theorem which describes direct images for homotopy and secondary invariants of Fréchet m-algebras under finitely summable quasihomomorphisms. The second aim is to provide local formulas which allow the explicit computation of direct images in many concrete cases. In particular we obtain a bivariant generalization of the Connes-Moscovici residue formula, and explain the link with chiral anomalies in quantum field theory.
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