{
  "abstract": "We construct smooth collapsing sequences with sectional curvature at least $-1$ whose limits are topological manifolds with nonzero Kirby--Siebenmann class. For every $n\\geq6$, the source and limit are simply connected, have dimensions $n+3$ and $n$, and the metrics have a common positive Ricci lower bound. The limits are homeomorphic to the product of the Chern four-manifold with $S^{n-4}$. We also obtain spin examples and five-dimensional lens-space homotopy types, the latter from finite quotients of one fixed $2$-connected eight-manifold. Finally, we realize aspherical manifolds with no closed PL representatives of their homotopy types as collapsing limits with scalar curvatures tending uniformly to $+\\infty$, and establish an obstruction to their approximation with almost nonnegative Ricci curvature.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05117",
  "author_total": 2,
  "authors": [
    {
      "name": "Jian Ge"
    },
    {
      "name": "Chao Qian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9mp6t0dy63rbp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05117",
  "fulltext_url": null,
  "id": "9mp6t0dy63rbp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05117",
  "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"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7220716368",
  "pdf_url": "https://arxiv.org/pdf/2610.05117",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9mp6t0dy63rbp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05117",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05117"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Collapse to nonsmoothable manifolds under lower sectional and positive Ricci curvature bounds",
  "title_text": "Collapse to nonsmoothable manifolds under lower sectional and positive Ricci curvature bounds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/9mp6t0dy63rbp",
  "venue": "arXiv",
  "versions": []
}