Secondary Invariants for Frechet Algebras and Quasihomomorphisms

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.

2000 Mathematics Subject Classification: 19D55, 19K56, 46L80, 46L87.

Keywords and Phrases: $K$-theory, bivariant cyclic cohomology, index theory.

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