{
  "abstract": "Let $N$ be a 3-dimensional integral homology sphere. We prove the existence of a sequence of 4-dimensional topologically negatively curved manifolds $M_k$, $k=1,2,\\dots$, satisfying the following: (1) all aspherical manifolds $M_k$ have the same universal cover $U_N$ depending only on $N$; (2) all fundamental groups $π_1(M_k)$ are hyperbolic and share the same Gromov boundary $X_N$ depending only on $N$; (3) the groups $π_1(M_k)$ represent infinitely many distinct quasi-isometry classes. The last conclusion, which represents the new feature, shows that negatively curved geometries in dimension 4 exhibit substantially richer structure than those in dimension 3.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15406",
  "author_total": 1,
  "authors": [
    {
      "name": "Jiming Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bapqdarkt4fhb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15406",
  "fulltext_url": null,
  "id": "bapqdarkt4fhb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15406",
  "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.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7221787912",
  "pdf_url": "https://arxiv.org/pdf/2610.15406",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bapqdarkt4fhb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15406",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15406"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "One boundary, infinitely geometries",
  "title_text": "One boundary, infinitely geometries",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/bapqdarkt4fhb",
  "venue": "arXiv",
  "versions": []
}