{
  "abstract": "We construct classical noncollapsed Ricci limits with a topologically singular point whose unique tangent cone has a topologically Euclidean vertex. Fix an integer $n\\ge4$ and a closed connected oriented smooth manifold $Q^n$ such that, for some smoothly embedded closed $n$-disc $D^n\\subset Q$, $Q\\setminus\\operatorname{int}D^n$ carries a positive-Ricci metric with unit-round strictly convex boundary. For all sufficiently small $q>0$, there is a complete pointed $(n+1)$-dimensional Gromov--Hausdorff limit $(Y,d,p)$, realized by complete smooth boundaryless $(n+1)$-manifolds with nonnegative Ricci curvature and uniformly positive based unit-ball volumes, with unique tangent cone $\\R^{n-1}\\times\\Cone(S^1_{2\\pi q})$ at $p$, where $\\Cone(S^1_{2\\pi q})$ is the cone over the circle of length $2\\pi q$. A neighbourhood of $p$ is homeomorphic to the open topological cone over $Q\\#(-Q)$, where $-Q$ has opposite orientation, and $H_j(Y,Y\\setminus\\{p\\};A)\\cong\\widetilde H_{j-1}(Q\\#(-Q);A)$ for every abelian group $A$ and $j\\ge0$. If $Q\\#(-Q)$ is not an integral homology $n$-sphere, then $p$ is topologically singular. At $p$, the density is $q$, and $Y$ has empty Kapovitch--Mondino boundary. For each integer $N\\ge5$, there is an $N$-dimensional example where $p$ is the unique nonmanifold point and every tangent cone at every point splits $\\R^{N-2}$. Thus the Cheeger--Colding codimension-four singular stratum is empty although $Y$ is not a topological manifold, disproving the Cheeger--Colding conjecture that the interior of its complement is a topological manifold.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Nifa Anass"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dy6qfr829s502.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.22670411",
  "fulltext_url": null,
  "id": "dy6qfr829s502",
  "issns": [],
  "landing_url": "https://hal.science/hal-05746087v2",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-dg"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05746087/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dy6qfr829s502.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:43Z",
      "native_id": "hal-05746087",
      "source": "hal",
      "url": "https://hal.science/hal-05746087v2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-dg",
      "subfield": "geometry-topology"
    }
  ],
  "title": "TOPOLOGICAL SINGULARITIES IN THE CODIMENSION-TWO STRATUM OF NONCOLLAPSED RICCI LIMITS",
  "title_text": "TOPOLOGICAL SINGULARITIES IN THE CODIMENSION-TWO STRATUM OF NONCOLLAPSED RICCI LIMITS",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:43Z",
  "url": "https://research.draconitic.com/paper/dy6qfr829s502",
  "venue": "HAL",
  "versions": []
}