On longitudinal differential operators and Nash blowups
Abstract
In this short note, we describe the Helffer–Nourrigat cone [HN80, AMY22] of a singular foliation in terms of the Nash algebroid associated to the foliation [Moh21, Lou23]. 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 F, generalizing results previously known in the literature.
Fields of Study & Subjects
Advanced Topics in Algebra
Advanced Operator Algebra Research
advanced mathematical theories
Publication details
- Journal / source
- Differential Geometry and its Applications
- Publisher
- Elsevier BV
- Volume
- 103
- Pages
- 102384–102384
- Publication date
- 21 April 2026
- Language
- EN