{
  "abstract": "We investigate étale Hausdorff groupoids whose source fibres have controlled growth with respect to a length function. Our first result shows that uniform subexponential growth implies topological amenability. If the unit space is compact and metrizable and such a length satisfies a suitable uniform doubling condition, then the groupoid has weak $m$-comparison for some $m$. For minimal ample groupoids, this implies comparison and almost unperforation of the type semigroup. Under the additional assumption that the unit space has no isolated points, we deduce Matui's AH-conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.16013",
  "author_total": 2,
  "authors": [
    {
      "name": "Are Austad"
    },
    {
      "name": "Christian Bönicke"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7jhzwwn2hvbxf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.16013",
  "fulltext_url": null,
  "id": "7jhzwwn2hvbxf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.16013",
  "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.DS"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7161565620",
  "pdf_url": "https://arxiv.org/pdf/2605.16013",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7jhzwwn2hvbxf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2605.16013",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.16013"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Growth Conditions for Étale Groupoids: Amenability and Comparison",
  "title_text": "Growth Conditions for Étale Groupoids: Amenability and Comparison",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/7jhzwwn2hvbxf",
  "venue": "arXiv",
  "versions": []
}