{
  "abstract": "Let $A$ be a unital, simple, separable, and pure $C^*$-algebra. We prove that, for every $a\\in A_+$, the set of positive elements in $A$ having the same Cuntz class as $a$ is path-connected. This may be viewed as a generalization to positive elements of the classical homotopy theory of projection classes and extends a line of results on the topology of constant Cuntz classes that previously required stronger regularity hypotheses to the class of pure $C^*$-algebras, which notably contains all selfless algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12219",
  "author_total": 2,
  "authors": [
    {
      "name": "Chrisil Ouseph"
    },
    {
      "name": "Andrew S. Toms"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/89hfk3c542061.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12219",
  "fulltext_url": null,
  "id": "89hfk3c542061",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12219",
  "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.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7221146416",
  "pdf_url": "https://arxiv.org/pdf/2610.12219",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/89hfk3c542061.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12219",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12219"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Homotopies of constant Cuntz classes in pure $C^*$-algebras",
  "title_text": "Homotopies of constant Cuntz classes in pure C^*-algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/89hfk3c542061",
  "venue": "arXiv",
  "versions": []
}