{
  "abstract": "In this paper, we study the rational realization of the gap-two product $K(\\mathbb{Q},n)\\times K(\\mathbb{Q},n+2)$ as the classifying space $B\\mathrm{aut}_1(X)$ for a simply-connected $π$-finite space $X$ with rational homology of finite type. We prove that $K(\\mathbb{Q},n)\\times K(\\mathbb{Q},n+2)$ can be realized as $B\\mathrm{aut}_1(X)$ up to rational homotopy equivalence if and only if $n=3,4$ or $4m+2$ for $m\\geq 1$. Moreover, we determine all their minimal Sullivan models up to isomorphism. The rational homotopy type of such $X$ is unique for $n=3$ or $4m+2$ for $m\\geq 1$; there exist infinitely many rational homotopy types of such $X$ for $n=4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11671",
  "author_total": 3,
  "authors": [
    {
      "name": "Yang Bai"
    },
    {
      "name": "Xiugui Liu"
    },
    {
      "name": "Jiaxi Zha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1jdkf9p09c4db.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11671",
  "fulltext_url": null,
  "id": "1jdkf9p09c4db",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11671",
  "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.AT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7221133404",
  "pdf_url": "https://arxiv.org/pdf/2610.11671",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1jdkf9p09c4db.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.11671",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11671"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A complete classification of the rational realization of gap-two products of Eilenberg--MacLane spaces as classifying spaces",
  "title_text": "A complete classification of the rational realization of gap-two products of Eilenberg--MacLane spaces as classifying spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/1jdkf9p09c4db",
  "venue": "arXiv",
  "versions": []
}