{
  "abstract": "We construct a marked integral delooping of a connected quandle's covering monoid, realizing its rack space as a homotopy fiber. For finite connected quandles at primes $p$ not dividing a point-stabilizer order, we determine the local $A_\\infty$ type and the ordinary rack cohomology shuffle algebra over fields of characteristic $p$. We compute integral quandle homology in all positive degrees for finite connected regular cyclic Alexander quandles and the tetrahedral quandle. At such primes dividing the quandle order, rack-space homotopy groups have exponentially many cyclic direct summands of fixed $p$-power order in each sufficiently large degree.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38066",
  "author_total": 1,
  "authors": [
    {
      "name": "Takefumi Nosaka"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6tp1e0z11x50x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38066",
  "fulltext_url": null,
  "id": "6tp1e0z11x50x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38066",
  "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.GT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38066",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6tp1e0z11x50x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38066",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38066"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Loop Space Models and Integral Homology of Connected Quandles",
  "title_text": "Loop Space Models and Integral Homology of Connected Quandles",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/6tp1e0z11x50x",
  "venue": "arXiv",
  "versions": []
}