On longitudinal differential operators and Nash blowups
arXiv:2509.01133 · doi:10.1016/j.difgeo.2026.102384
Abstract
In this short note, we describe the Helffer-Nourrigat cone of a singular foliation in terms of the Nash algebroid associated to the foliation. Along the way, we show that the Helffer-Nourrigat cone is a union of symplectic leaves of the canonical Poisson structures on the dual of the holonomy Lie algebroids. We also provide, within this framework, a characterization of longitudinally elliptic differential operators on a singular foliation , generalizing results previously known in the literature.
We have corrected some typographical errors in the text and added several clarifications
References in corpus (8)
- Lie-Rinehart algebras, descent, and quantization
- Almost Lie Algebroids and Characteristic Classes
- On the history of Lie brackets, crossed modules, and Lie-Rinehart algebras
- On the universal enveloping algebra of a Lie-Rinehart algebra
- A pseudodifferential calculus for maximally hypoelliptic operators and the Helffer-Nourrigat conjecture
- Blow-up groupoid of singular foliations
- Geometric tool kit for higher spin gravity (part II): An introduction to Lie algebroids and their enveloping algebras
- On Nash resolution of (singular) Lie algebroids