{
  "abstract": "Let $A$ and $X$ be connected based CW complexes with $H_1(A;\\mathbb Q)\\neq 0$, and let $m\\geq 1$ be the least degree with $\\widetilde H_m(X;\\mathbb Q)\\neq0$. We prove that the Bousfield--Kan rational completion map of $A\\vee X$ induces a map on $H_{2m}(-;\\mathbb Q)$ whose cokernel has dimension at least $2^{\\aleph_0}$. In particular, $A\\vee X$ is $\\mathbb Q$-bad.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12255",
  "author_total": 1,
  "authors": [
    {
      "name": "Nikita Golub"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1c944zycwrd6v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12255",
  "fulltext_url": null,
  "id": "1c944zycwrd6v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12255",
  "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.AT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7221190483",
  "pdf_url": "https://arxiv.org/pdf/2610.12255",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1c944zycwrd6v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12255",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12255"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Wedges, Rational completion and $\\mathbb Q$-bad spaces",
  "title_text": "Wedges, Rational completion and ℚ-bad spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/1c944zycwrd6v",
  "venue": "arXiv",
  "versions": []
}