English

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}
}