{
  "abstract": "We prove an equivariant version of the theorem of Hector, Mac\\'ıas-Virgós, and Sanmart\\'ın-Carbón identifying diffeological forms on the leaf space of a foliation with basic forms. For any group $K$ acting by foliation-preserving diffeomorphisms, we show that this identification is an isomorphism of $K$-equivariant cochain complexes. We then establish a descent theorem for basic differential forms under locally free Lie group actions without assuming properness. Let a Lie group $H$, not necessarily connected or second countable, act smoothly and locally freely on a second countable manifold $M$, and let $\\mathcal F$ be the foliation by $H_0$-orbits. We prove that pullback induces an isomorphism \\[ Ω^\\bullet(M/H)\\congΩ^\\bullet(M,\\mathcal F)^H \\] provided that $H$ is second countable or that the induced action of $H/H_0$ on $M/H_0$ satisfies a natural subduction condition. We also give a smooth free action for which descent fails, showing that an additional hypothesis is genuinely necessary.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.01891",
  "author_total": 1,
  "authors": [
    {
      "name": "Yi Lin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bspsch2sq74j1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.01891",
  "fulltext_url": null,
  "id": "bspsch2sq74j1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.01891",
  "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.SG"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7160305021",
  "pdf_url": "https://arxiv.org/pdf/2605.01891",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bspsch2sq74j1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2605.01891",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.01891"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Descent of Basic Forms to Quotients by Locally Free Lie Group Actions",
  "title_text": "Descent of Basic Forms to Quotients by Locally Free Lie Group Actions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/bspsch2sq74j1",
  "venue": "arXiv",
  "versions": []
}