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arXiv · 2509.01133

On longitudinal differential operators and Nash blowups

Ruben Louis
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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 $\mathcal{F}$, generalizing results previously known in the literature.

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Ruben Louis. 2025-09-01. On longitudinal differential operators and Nash blowups. https://doi.org/10.1016/j.difgeo.2026.102384

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