{
  "abstract": "In this paper, for various pairs of topological spaces $X$ and $Y$, we introduce an analogue of the Bernšte\\uın-Gel'fand-Ponomarev reflection functors between the categories of C*-algebras over $X$ and $Y$. We prove that these functors induce equivalences $\\mathfrak{KK}(X)_{\\mathrm{loc}} \\simeq \\mathfrak{KK}(Y)_{\\mathrm{loc}}$ between Meyer and Nest's localizing subcategories in Kirchberg's ideal-related KK-theory, and $\\mathfrak{E}(X) \\simeq \\mathfrak{E}(Y)$ between the entire categories in Dadarlat and Meyer's ideal-related E-theory. Both equivalences restrict to the respective bootstrap categories: $\\mathcal{B}(X) \\simeq \\mathcal{B}(Y)$ and $\\mathcal{B}_{\\mathrm{E}}(X) \\simeq \\mathcal{B}_{\\mathrm{E}}(Y)$. Combining these equivalences with a combinatorial argument in quiver representation theory, we obtain the same equivalences for any two finite $T_0$-spaces whose Hasse diagrams are orientations of the same tree. Moreover, we prove a rearrangement property of reflection functors, which yields an analogue of Coxeter functors. Finally, we apply reflection functors to give a conceptual alternative proof of Bentmann and Köhler's universal coefficient theorem for filtrated K-theory over finite $T_0$-spaces whose Hasse diagrams are orientations of Dynkin diagrams of type A.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.22317",
  "author_total": 1,
  "authors": [
    {
      "name": "Nanami Hashimoto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/atq2v5kettwsg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.22317",
  "fulltext_url": null,
  "id": "atq2v5kettwsg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.22317",
  "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"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
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  ],
  "openalex": "W7204187938",
  "pdf_url": "https://arxiv.org/pdf/2608.22317",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/atq2v5kettwsg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2608.22317",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.22317"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.KT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Equivalence of categories of bivariant K-theory for C*-algebras over topological spaces via reflection functors",
  "title_text": "Equivalence of categories of bivariant K-theory for C*-algebras over topological spaces via reflection functors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/atq2v5kettwsg",
  "venue": "arXiv",
  "versions": []
}