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Secondary invariants for Frechet algebras and quasihomomorphisms. (English) Zbl 1149.19005

Author’s 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.

MSC:

19D55 \(K\)-theory and homology; cyclic homology and cohomology
19K56 Index theory
46L80 \(K\)-theory and operator algebras (including cyclic theory)
46L87 Noncommutative differential geometry
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