2011/03/31 by Grensing, Martin
#FOS: Mathematics #FOS: Physical sciences #K-Theory and Homology (math.KT) #Mathematical Physics (math-ph) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1103.6245
We give a simple proof of the smooth Thom isomorphism for complex bundles for the bivariant K-theories on locally convex algebras considered by Cuntz. We also prove the Thom isomorphism in Kasparov's KK-theory in a form stated without proof in the conspectus. Along the way, we prove Bott periodicity directly on Rn, using for the Kasparov product the operator that also appears in recent work of Wulkenhaar on non-compact spectral triples with finite volume, and which may be seen as a unitalisation of the Dirac-element.