{
  "abstract": "Let $M$ be a complete open $5$-manifold with nonnegative Ricci curvature. If its universal cover $\\tilde M$ has Euclidean volume growth, then $π_1(M)$ is finitely generated and virtually $\\mathbb Z^k$ for some $0\\le k\\le4$. This confirms a conjecture of Pan and Rong \\cite{PR18} in dimension five; see also \\cite{BNS25,BrNaSe25}. In dimension six, under the same volume growth assumption, we also obtain a quantitative virtual abelianness result without assuming finite generation of the fundamental group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09080",
  "author_total": 1,
  "authors": [
    {
      "name": "Hongzhi Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/87en21f1zcj5v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09080",
  "fulltext_url": null,
  "id": "87en21f1zcj5v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09080",
  "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.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212000278",
  "pdf_url": "https://arxiv.org/pdf/2609.09080",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/87en21f1zcj5v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2609.09080",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09080"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Fundamental Groups in the Five Dimensional Pan-Rong Conjecture",
  "title_text": "Fundamental Groups in the Five Dimensional Pan-Rong Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/87en21f1zcj5v",
  "venue": "arXiv",
  "versions": []
}