The Thom isomorphism in bivariant Ktheory
Abstract
We give a simple proof of the smooth Thom isomorphism for complex bundles for the bivariant Ktheories on locally convex algebras considered by Cuntz. We also prove the Thom isomorphism in Kasparov's KKtheory in a form stated without proof in the conspectus. Along the way, we prove Bott periodicity directly on R^n, using for the Kasparov product the operator that also appears in recent work of Wulkenhaar on noncompact spectral triples with finite volume, and which may be seen as a unitalisation of the Diracelement.
 Publication:

arXiv eprints
 Pub Date:
 March 2011
 arXiv:
 arXiv:1103.6245
 Bibcode:
 2011arXiv1103.6245G
 Keywords:

 Mathematics  KTheory and Homology;
 Mathematical Physics;
 Mathematics  Operator Algebras