Pseudodifferential operators on filtered manifolds

Filtered manifolds allow to attach orders greater than one to vector fields when understood as differential operators. As a consequence, the highest order part of an operator belongs to a noncommutative algebra. Instead of the principal symbol, one considers a family of operators acting on certain osculating Lie groups. In this talk, I will explain how the order zero pseudodifferential extension of this calculus can be obtained using generalized fixed point algebras. I will discuss how the Rockland condition on the osculating groups yields a criterion when an operator is Fredholm.

This talk is based on my recently completed PhD thesis supervised by Ralf Meyer and Ryszard Nest.