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We use filtrations of the tangent bundle of a manifold starting with anintegrable subbundle to define transverse symbols to the correspondingfoliation, define a condition of transversally Rockland and prove thattransversally Rockland operators yield a K-homology class. We construct anequivariant KK-class for transversally Rockland transverse symbols and show aPoincare duality type result linking the class of an operator and its symbol.

A transverse index theorem in the calculus of filtered manifolds