{
  "abstract": "Let $G$ and $H$ be compactly generated totally disconnected locally compact (tdlc) groups that decompose as finite graphs of tdlc groups $(\\mathcal{G}, \\mathcal{A})$ and $(\\mathcal{H}, \\mathcal{B})$ such that all edge groups are compact and all vertex groups have at most one end. We generalize a result of Papasoglu--Whyte to tdlc groups and show that $G$ and $H$ are quasi-isometric if and only if they have the same number of ends and every one-ended vertex group of $(\\mathcal{G}, \\mathcal{A})$ is quasi-isometric to a one-ended vertex group of $(\\mathcal{H}, \\mathcal{B})$, and vice versa. As an application, we construct uncountably many pairwise non-quasi-isometric compactly generated non-discrete simple tdlc groups, strengthening a result by Smith.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30881",
  "author_total": 1,
  "authors": [
    {
      "name": "Sebastian Giersbach"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/20a3pkmepyd9e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30881",
  "fulltext_url": null,
  "id": "20a3pkmepyd9e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30881",
  "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.GR"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7204914950",
  "pdf_url": "https://arxiv.org/pdf/2608.30881",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/20a3pkmepyd9e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2608.30881",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30881"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Quasi-isometries between graphs of totally disconnected locally compact groups",
  "title_text": "Quasi-isometries between graphs of totally disconnected locally compact groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/20a3pkmepyd9e",
  "venue": "arXiv",
  "versions": []
}