A transverse index theorem in the calculus of filtered manifolds

Clément Cren

doi:10.1016/j.jfa.2024.110618

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arXiv · 2207.09112

A transverse index theorem in the calculus of filtered manifolds

Clément Cren

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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.

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Clément Cren. 2022-07-19. A transverse index theorem in the calculus of filtered manifolds. https://doi.org/10.1016/j.jfa.2024.110618

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