On longitudinal differential operators and Nash blowups
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911650797322240 |
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| author | Louis, Ruben |
| author_facet | Louis, Ruben |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01133 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On longitudinal differential operators and Nash blowups Louis, Ruben Differential Geometry 53-XX, 53D17, 32S45 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. |
| title | On longitudinal differential operators and Nash blowups |
| topic | Differential Geometry 53-XX, 53D17, 32S45 |
| url | https://arxiv.org/abs/2509.01133 |