{
  "abstract": "We give a direct differential-geometric proof of a result of Crainic on the cohomology of pullbacks of Lie algebroids under surjective submersions: If the fibers are connected and have vanishing cohomology through degree $n$, pullback with coefficients in any representation is an isomorphism through degree $n$ and is injective in degree $n+1$. The proof reduces to a vanishing result for leafwise cohomology and uses an exhaustion-and-patching argument due to Buchdahl. No local triviality or finite-type assumption on the fibers is required. We also prove the analogous result for holomorphic Lie algebroids.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: SIGMA 22 (2026), 107, 13 pages",
  "arxiv": "2607.23859",
  "author_total": 1,
  "authors": [
    {
      "name": "Eckhard Meinrenken"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4p0xrd48fhy6k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.23859",
  "fulltext_url": null,
  "id": "4p0xrd48fhy6k",
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  "landing_url": "https://arxiv.org/abs/2607.23859",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7171512457",
  "pdf_url": "https://arxiv.org/pdf/2607.23859",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4p0xrd48fhy6k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2607.23859",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.23859"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A note on the cohomology of pullback Lie algebroids",
  "title_text": "A note on the cohomology of pullback Lie algebroids",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:42Z",
  "url": "https://research.draconitic.com/paper/4p0xrd48fhy6k",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.3842/sigma.2026.107",
      "pid": "5rbwwmj9f7zpg",
      "relation": "published-as",
      "title": "A Note on the Cohomology of Pullback Lie Algebroids",
      "venue": "Symmetry, Integrability and Geometry: Methods and Applications"
    }
  ]
}