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

Bertrand Monthubert (1) , Victor Nistor (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 Departement of Mathematics

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.

Mots clés: Comparison algebra; Index theory; Manifolds with corners

Domaines: K-théorie et homologie [math.KT]; Algèbres d'opérateurs [math.OA]

Bertrand Monthubert, Victor Nistor. The $K$-groups and the index theory of certain comparison $C^*$-algebras. Contemp. Math., 2011, 546, pp.213-224. ⟨hal-00474026⟩