A transverse index theorem in the calculus of filtered manifolds

Abstract

We use filtrations of the tangent bundle of a manifold starting with an integrable subbundle to define transverse symbols to the corresponding foliation, define a condition of transversally Rockland and prove that transversally Rockland operators yield a K-homology class. We construct an equivariant KK-class for transversally Rockland transverse symbols and show a Poincare duality type result linking the class of an operator and its symbol.

References in corpus (3)

• Index theorem for inhomogeneous hypoelliptic differential operators
• Pseudodifferential operators on filtered manifolds as generalized fixed points
• A pseudodifferential calculus for maximally hypoelliptic operators and the Helffer-Nourrigat conjecture