Universal cycles and homological invariants of locally convex algebras

Details Universal cycles and homological invariants of locally convex algebras Universal cycles and homological invariants of locally convex algebras

2011-03-31

arxiv.org/abs/1103.6243v2

Mathematics

K-Theory and Homology

Scientific paper

Using an appropriate notion of locally convex Kasparov modules, we show how to induce isomorphisms under a large class of functors on the category of locally convex algebras; examples are obtained from spectral triples. Our considerations are based on the action of algebraic K-theory on these functors, and involve compatibility properties of the induction process with this action, and with Kasparov-type products. This is based on an appropriate interpretation of the Connes-Skandalis connection formalism. As an application, we prove Bott periodicity and a Thom isomorphism for algebras of Schwartz functions.

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