{
  "abstract": "We give a negative answer to a question of Sánchez Saldaña--Velásquez and Lück asking whether the topological K-theory of the reduced group C*-algebra of a split crystallographic group with finite cyclic holonomy is always torsion-free. For two explicit split crystallographic groups with translation subgroup of rank four and holonomy of order four, we compute the equivariant K-theory of the classifying space for proper actions and find nontrivial two-torsion. The equivariant universal coefficient theorem transfers this torsion to proper equivariant K-homology, and the Baum--Connes conjecture identifies the resulting groups with the topological K-theory of the corresponding reduced group C*-algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00493",
  "author_total": 2,
  "authors": [
    {
      "name": "Cristian Sarmiento"
    },
    {
      "name": "Mario Velasquez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b0kpkp7hzy4kc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00493",
  "fulltext_url": null,
  "id": "b0kpkp7hzy4kc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00493",
  "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.KT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00493",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b0kpkp7hzy4kc.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00493",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00493"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.KT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Counterexamples to torsion-freeness in the $K$-theory of crystallographic group $C^*$-algebras",
  "title_text": "Counterexamples to torsion-freeness in the K-theory of crystallographic group C^*-algebras",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/b0kpkp7hzy4kc",
  "venue": "arXiv",
  "versions": []
}