A transverse index theorem in the calculus of filtered manifolds
Differential Geometry
2025-03-13 v2 K-Theory and Homology
Operator Algebras
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.
Keywords
Cite
@article{arxiv.2207.09112,
title = {A transverse index theorem in the calculus of filtered manifolds},
author = {Clément Cren},
journal= {arXiv preprint arXiv:2207.09112},
year = {2025}
}