C*-algebra of a differential groupoid
Categorical differential geometry
Commutator representations of covariant differential calculi
Complex structure on the smooth dual of .
Contribution of noncommutative geometry to index theory on singular manifolds
This survey of the work of the author with several collaborators presents the way groupoids appear and can be used in index theory. We define the general tools, and apply them to the case of manifolds with corners, ending with a topological index theorem.