Universal cycles and homological invariants of locally convex algebras |
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Authors: | Martin Grensing |
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Institution: | Institut de Mathématiques de Jussieu, Projet Algèbres d?Opérateurs, 175 rue du Chevaleret, 75013 Paris, France |
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Abstract: | 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. As a special case, this applies to the theories kk for locally convex algebras considered by Cuntz. |
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