{
  "abstract": "For every closed oriented smooth four-manifold $M$ admitting a metric of strictly negative sectional curvature, we prove that $\\dim_{\\mathbb{Q}}H_1(T(M);\\mathbb{Q})=\\dim_{\\mathbb{Q}}H_1(T_{\\mathrm{TOP}}(M);\\mathbb{Q})=\\infty$ where $T(M)$ and $T_{\\mathrm{TOP}}(M)$ denote the Torelli groups. This extends a theorem of Budney--Gabai for real hyperbolic manifolds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24562",
  "author_total": 1,
  "authors": [
    {
      "name": "Weizhe Niu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/779rf67bsq5m4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24562",
  "fulltext_url": null,
  "id": "779rf67bsq5m4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24562",
  "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.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7214050671",
  "pdf_url": "https://arxiv.org/pdf/2609.24562",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/779rf67bsq5m4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24562",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24562"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Mapping class groups of negatively curved four-manifolds",
  "title_text": "Mapping class groups of negatively curved four-manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/779rf67bsq5m4",
  "venue": "arXiv",
  "versions": []
}