Secondary invariants for Frechet algebras and quasihomomorphisms

Abstract

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 $K$-theory and the non-periodic versions of cyclic homology). The aim of this paper is to establish a Riemann-Roch-Grothendieck theorem relating direct images for homotopy and secondary invariants of Fréchet $m$-algebras under finitely summable quasihomomorphisms.