{
  "abstract": "For a uniformly locally finite coarse space $X$, the uniform Roe algebra $C_u^*(X)$ is the operator norm closure of the controlled operators on $\\ell^2(X)$. The $K$-theory of uniform Roe algebras is known in asymptotic dimension zero, but it is not fully understood in higher dimensions. We compute $K_0(C_u^*(G,\\mathcal E))$ and $K_1(C_u^*(G,\\mathcal E))$ for every countable discrete abelian group $G$ and every finite-rank free abelian subgroup $H\\leq G$, where $\\mathcal E$ is the coarse structure generated by $H$. We use the Proietti--Yamashita spectral sequence to express the $K$-theory in terms of $H_*(H;\\ell^\\infty(G,\\mathbb Z))$, which we then compute.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06305",
  "author_total": 2,
  "authors": [
    {
      "name": "Charles Fanning"
    },
    {
      "name": "Mehmet Emin Aktas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/69kpxnd7sybxm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06305",
  "fulltext_url": null,
  "id": "69kpxnd7sybxm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06305",
  "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.KT"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7212034544",
  "pdf_url": "https://arxiv.org/pdf/2609.06305",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/69kpxnd7sybxm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06305",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06305"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.KT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The K-theory of uniform Roe algebras for coarse structures generated by finite-rank free abelian subgroups",
  "title_text": "The K-theory of uniform Roe algebras for coarse structures generated by finite-rank free abelian subgroups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/69kpxnd7sybxm",
  "venue": "arXiv",
  "versions": []
}