The $K$-groups and the index theory of certain comparison $C^*$-algebras
K-Theory and Homology
2010-05-12 v1 Classical Analysis and ODEs
Operator Algebras
Abstract
We compute the -theory of comparison -algebra associated to a manifold with corners. These comparison algebras are an example of the abstract pseudodifferential algebras introduced by Connes and Moscovici \cite{M3}. Our calculation is obtained by showing that the comparison algebras are a homomorphic image of a groupoid -algebra. We then prove an index theorem with values in the -theory groups of the comparison algebra.
Keywords
Cite
@article{arxiv.1005.1718,
title = {The $K$-groups and the index theory of certain comparison $C^*$-algebras},
author = {Bertrand Monthubert and Victor Nistor},
journal= {arXiv preprint arXiv:1005.1718},
year = {2010}
}
Comments
15 pages