The Thom isomorphism in bivariant K-theory
K-Theory and Homology
2011-04-01 v1 Mathematical Physics
math.MP
Operator Algebras
Abstract
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 R^n, 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.
Cite
@article{arxiv.1103.6245,
title = {The Thom isomorphism in bivariant K-theory},
author = {Martin Grensing},
journal= {arXiv preprint arXiv:1103.6245},
year = {2011}
}