{
  "abstract": "Let $G \\rightrightarrows G^{(0)}$ be a Lie groupoid, $\\mathrm{A} G \\rightarrow G^{(0)}$ its Lie algebroid and $X_1, \\dots, X_r$ a family of sections of $\\mathrm{A} G$ satisfying a Lie bracket generating condition of Hörmander type. We aim to build a pseudodifferential calculus allowing to study a Helffer-Nourrigat's conjecture on the groupoid $G$; in particular, we want differential operators of the form $\\sum_{i = 1}^r X_i^2$ to have an invertible symbol. In this article we achieve the geometrical part of this construction by defining a \"weighted\" version of the deformation to the normal cone $\\mathrm{DNC}(G, G^{(0)}) \\rightrightarrows G^{(0)} \\times \\mathbb{R}_+$. Heuristically, we deform $G$ around $G^{(0)}$ with a \"zoom\" parameter $t \\in \\mathbb{R}_+$ by stretching $G$ by $t$ in the directions of the sections $X_i$, $t^2$ along $[X_i, X_j]$, $t^3$ along $[X_i, [X_j, X_k]]$ etc. In the case where $G = M \\times M$ we recover a construction of Mohsen, and when the structure is equiregular we recover a construction of van Erp-Yuncken.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29331",
  "author_total": 1,
  "authors": [
    {
      "name": "Paul Le Breton"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0c3nyvr1rbjcz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29331",
  "fulltext_url": null,
  "id": "0c3nyvr1rbjcz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29331",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7214373732",
  "pdf_url": "https://arxiv.org/pdf/2609.29331",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0c3nyvr1rbjcz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29331",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29331"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Filtered deformations of Lie groupoids",
  "title_text": "Filtered deformations of Lie groupoids",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/0c3nyvr1rbjcz",
  "venue": "arXiv",
  "versions": []
}