{
  "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": [
    "University of Toronto, Canada"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Eckhard Meinrenken"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5rbwwmj9f7zpg.bib",
  "cited_by": 0,
  "doi": "10.3842/sigma.2026.107",
  "fulltext_url": null,
  "id": "5rbwwmj9f7zpg",
  "issns": [
    "1815-0659"
  ],
  "landing_url": "https://sigma-journal.com/2026/107/",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by-sa/4.0/",
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  "native_subjects": [],
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  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": "SIGMA (Symmetry, Integrability and Geometry: Methods and Application)",
  "ris": "https://research.draconitic.com/paper/5rbwwmj9f7zpg.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T00:20:49Z",
      "native_id": "10.3842/sigma.2026.107",
      "source": "crossref",
      "url": "https://sigma-journal.com/2026/107/"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:1815-0659",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "A Note on the Cohomology of Pullback Lie Algebroids",
  "title_text": "A Note on the Cohomology of Pullback Lie Algebroids",
  "type": "peer-reviewed",
  "updated_at": "2026-11-06T00:21:05Z",
  "url": "https://research.draconitic.com/paper/5rbwwmj9f7zpg",
  "venue": "Symmetry, Integrability and Geometry: Methods and Applications",
  "versions": [
    {
      "doi": "10.48550/arxiv.2607.23859",
      "pid": "4p0xrd48fhy6k",
      "relation": "preprint",
      "title": "A note on the cohomology of pullback Lie algebroids",
      "venue": "arXiv"
    }
  ]
}