The $K$-groups and the index theory of certain comparison $C^*$-algebras

Details The $K$-groups and the index theory of certain comparison $C^*$-algebras The $K$-groups and the index theory of certain comparison $C^*$-algebras

2010-05-11

arxiv.org/abs/1005.1718v1

Mathematics

K-Theory and Homology

15 pages

Scientific paper

We compute the $K$-theory of comparison $C^*$-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 $C^*$-algebra. We then prove an index theorem with values in the $K$-theory groups of the comparison algebra.

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