{
  "abstract": "We prove that closed arithmetic hyperbolic $n$-manifolds of bounded rank have bounded adjoint trace field degree, and consequently have lower bounded injectivity radius. From this, we obtain a number of corollaries. In particular, we obtain that closed arithmetic hyperbolic $3$-manifolds of bounded rank are contained in finitely many commensurability classes, and describe these commensurability classes. Additionally, it follows that for closed arithmetic hyperbolic $3$-manifolds, Heegaard genus is equal to rank for all but finitely many manifolds of each rank.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18841",
  "author_total": 1,
  "authors": [
    {
      "name": "Matthew Zevenbergen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/89hm0naqctyhr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18841",
  "fulltext_url": null,
  "id": "89hm0naqctyhr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18841",
  "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.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7221807618",
  "pdf_url": "https://arxiv.org/pdf/2610.18841",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/89hm0naqctyhr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18841",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18841"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Arithmetic hyperbolic manifolds with bounded rank",
  "title_text": "Arithmetic hyperbolic manifolds with bounded rank",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/89hm0naqctyhr",
  "venue": "arXiv",
  "versions": []
}