{
  "abstract": "We show that if $N\\subset M$ is an inclusion of $\\mathrm{II}_1$ factors of uniform infinite index, for instance an irreducible inclusion of infinite index, then every positive contraction $b\\in N$ is of the form $E_N(p)$ for a projection $p\\in M$. This gives the exact version of Popa's asymptotic result in the ultrapower, and it is a subfactor analogue of the Carpenter problem for masas. In particular, Popa's relative dimension set of such an inclusion is $[0,1]$, so the set of expectations of projections does not distinguish inclusions without corners of finite index. As applications, the Carpenter property holds for $N\\subset N\\rtimes G$ whenever an infinite group $G$ acts outerly on a $\\mathrm{II}_1$ factor $N$, and for ICC groups $H\\le G$ the inclusion $L(H)\\subset L(G)$ has it exactly when $[G:H]=\\infty$, confirming a recent conjecture. We also give examples showing that the Carpenter property does not imply uniform infinite index, and that infinite index does not imply the Carpenter property.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02006",
  "author_total": 2,
  "authors": [
    {
      "name": "Dietmar Bisch"
    },
    {
      "name": "Julio Cáceres"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0rmq912wxk13r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02006",
  "fulltext_url": null,
  "id": "0rmq912wxk13r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02006",
  "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.OA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02006",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0rmq912wxk13r.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02006",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02006"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Carpenter property for subfactors of uniform infinite index",
  "title_text": "The Carpenter property for subfactors of uniform infinite index",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/0rmq912wxk13r",
  "venue": "arXiv",
  "versions": []
}