{
  "abstract": "We characterise coarse embeddability of box spaces into Hilbert space in terms of a-T-menability of the associated Higson-Lafforgue-Skandalis (HLS) groupoids. Moreover, we prove that a-T-menability and metric amenability are independent for HLS groupoids: all four possible combinations occur among HLS groupoids associated with approximating sequences of the free group $\\mathbb F_2$. The two separating examples are constructed using relative expansion and twisted spectral-gap techniques, respectively.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39479",
  "author_total": 4,
  "authors": [
    {
      "name": "Yu Qiao"
    },
    {
      "name": "Hao Song"
    },
    {
      "name": "Yan Wang"
    },
    {
      "name": "Jiawen Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4dtxv80t4efvw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39479",
  "fulltext_url": null,
  "id": "4dtxv80t4efvw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39479",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OA"
    ]
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39479",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4dtxv80t4efvw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39479",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39479"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A-T-menability and metric amenability for HLS groupoids",
  "title_text": "A-T-menability and metric amenability for HLS groupoids",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/4dtxv80t4efvw",
  "venue": "arXiv",
  "versions": []
}