{
  "abstract": "We generalize the concept of orbit-breaking from the case of a homeomorphism to the case of a surjective local homeomorphism. This method creates open subgroupoids of the Deaconu--Renualt groupoid associated to the surjective local homeomorphism. When the map satisfies natural assumptions (including being locally expanding) the resulting groupoid $\\mathrm{C}^*$-algebras are unital UCT Kirchberg algebras. A specific class of Deaconu--Renault systems are constructed, each modelling the Cuntz algebra $\\mathcal{O}_2$. The $\\mathrm{C}^*$-algebras obtained from orbit-breaking for such systems come with explicit embeddings into $\\mathcal{O}_2$. We also introduce a method for orbit-breaking after removing a fixed point. Using this method, we can realize all stable UCT Kirchberg algebras with each coming with an embeddings into $\\mathcal O_2\\otimes\\mathcal K$. Moreover, we show that, given a homomorphism between countable graded abelian groups, there is a $^*$-homomorphism between orbit-breaking algebras obtained from a groupoid inclusion. In particular, we obtain explicit $^*$-homomorphisms between stable UCT Kirchberg algebras from any group homomorphism between their $K$-groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31883",
  "author_total": 3,
  "authors": [
    {
      "name": "Robin J. Deeley"
    },
    {
      "name": "Ian F. Putnam"
    },
    {
      "name": "Karen R. Strung"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5hy0zhd5w35vs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31883",
  "fulltext_url": null,
  "id": "5hy0zhd5w35vs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31883",
  "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.DS"
    ],
    [
      "arxiv",
      "math.KT"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7214742194",
  "pdf_url": "https://arxiv.org/pdf/2609.31883",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5hy0zhd5w35vs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.31883",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31883"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.KT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Orbit-breaking in Deaconu-Renault groupoids and models for UCT Kirchberg algebras",
  "title_text": "Orbit-breaking in Deaconu-Renault groupoids and models for UCT Kirchberg algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/5hy0zhd5w35vs",
  "venue": "arXiv",
  "versions": []
}