{
  "abstract": "The landmark quantum complexity result MIP Superscript asterisk ∗ $^*$ equals = $=$ RE has been used to prove the existence of a non-Connes-embeddable tracial von Neumann algebra. Recently, similar ideas have been used to give a negative solution to the Aldous–Lyons conjecture: there is a non-co-sofic invariant random subgroup (IRS) on any non-abelian free group. We define a notion of hyperlinearity for an IRS and show that there is a non-co-hyperlinear IRS on any non-abelian free group. As a corollary, we prove that there is a relation whose von Neumann algebra is not Connes embeddable. We do this by significantly simplifying the reduction of Aldous–Lyons to non-local games, removing the need for subgroup tests entirely.",
  "abstract_shown": true,
  "affiliations": [
    "University of Waterloo"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Aareyan Manzoor",
      "orcid": "0009-0001-1623-2506"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eaxenkw9b8brp.bib",
  "cited_by": 11,
  "doi": "10.1017/s0010437x26103431",
  "fulltext_url": null,
  "id": "eaxenkw9b8brp",
  "issns": [
    "0010-437X",
    "1570-5846"
  ],
  "landing_url": "https://doi.org/10.1017/s0010437x26103431",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W4407359513",
  "pdf_url": "https://www.cambridge.org/core/services/aop-cambridge-core/content/view/62580DF5D8E0D2BB40EAFBA1174B6E33/S0010437X26103431a.pdf/div-class-title-there-is-an-equivalence-relation-whose-von-neumann-algebra-is-not-connes-embeddable-div.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-01",
  "publisher": "Cambridge University Press",
  "ris": "https://research.draconitic.com/paper/eaxenkw9b8brp.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T13:20:42Z",
      "native_id": "W4407359513",
      "source": "openalex",
      "url": "https://doi.org/10.1017/s0010437x26103431"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Advanced Operator Algebra Research",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "There is an equivalence relation whose von Neumann algebra is not Connes embeddable",
  "title_text": "There is an equivalence relation whose von Neumann algebra is not Connes embeddable",
  "type": "peer-reviewed",
  "updated_at": "2026-11-07T13:20:42Z",
  "url": "https://research.draconitic.com/paper/eaxenkw9b8brp",
  "venue": "Compositio Mathematica",
  "versions": []
}