{
  "abstract": "We study strict inverse systems of locally convex Lie groupoids and Lie algebroids. We show that strict inverse limits of Lie algebroids and Lie groupoids inherit natural Lie structures and establish a natural isomorphism of functors $\\varprojlim\\circ\\operatorname{Lie}\\cong\\operatorname{Lie}\\circ\\varprojlim$. We then consider inverse systems of integrable Banach-Lie algebroids and their source-simply connected levelwise integrations. We give conditions under which these integrations form a strict inverse system of Lie groupoids and hence their inverse limit integrates the inverse-limit algebroid. Under additional hypotheses on the source-fiber inverse sequence, we describe the obstruction to source-simply connectedness of the resulting integration in terms of the derived inverse limit $\\varprojlim^{1}π_2$ of the second homotopy groups of the source fibers. We illustrate the theory with several examples: inverse limits of jet groupoids, current groupoids, and gauge groupoids, including the corresponding inverse-limit Atiyah algebroids and a source-simply connected inverse-limit integration arising from the quaternionic Hopf bundle.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12296",
  "author_total": 1,
  "authors": [
    {
      "name": "Ahmed Gamal Shaltut"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a55zqh26szv4r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12296",
  "fulltext_url": null,
  "id": "a55zqh26szv4r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12296",
  "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"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7221130683",
  "pdf_url": "https://arxiv.org/pdf/2610.12296",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a55zqh26szv4r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.12296",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12296"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Inverse limits of locally convex Lie groupoids",
  "title_text": "Inverse limits of locally convex Lie groupoids",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/a55zqh26szv4r",
  "venue": "arXiv",
  "versions": []
}