Universal cycles and homological invariants of locally convex algebras
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 Ktheory on these functors, and involve compatibility properties of the induction process with this action, and with Kasparovtype products. This is based on an appropriate interpretation of the ConnesSkandalis connection formalism. As an application, we prove Bott periodicity and a Thom isomorphism for algebras of Schwartz functions.
 Publication:

arXiv eprints
 Pub Date:
 March 2011
 arXiv:
 arXiv:1103.6243
 Bibcode:
 2011arXiv1103.6243G
 Keywords:

 Mathematics  KTheory and Homology;
 Mathematics  Algebraic Topology;
 Mathematics  Operator Algebras