Secondary invariants for Frechet algebras and quasihomomorphisms

TL;DR

This paper explores secondary invariants in Frechet algebras, establishing a Riemann-Roch-Grothendieck theorem that links homotopy and secondary invariants under finitely summable quasihomomorphisms.

Contribution

It introduces a Riemann-Roch-Grothendieck theorem connecting direct images of homotopy and secondary invariants in Frechet m-algebras.

Findings

Established a Riemann-Roch-Grothendieck theorem for Frechet m-algebras.

Linked homotopy invariants with secondary invariants via quasihomomorphisms.

Provided a framework for understanding invariants in multiplicatively convex topologies.

Abstract

A Frechet 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 Frechet m-algebras under finitely summable quasihomomorphisms.