{
  "abstract": "The fundamental groups of compact $3$-manifolds are known to be residually finite. Feng Luo conjectured that a stronger statement is true, by allowing only finite groups of the form $\\mathrm{PGL}_2(R),$ where $R$ is a finite commutative ring with identity. In a prior paper, \"Linear representations of $3$-manifold groups over rings\", we, together with two co-authors, gave an equivalent formulation of Luo's conjecture via faithful representations, investigated variants of the conjecture where the target group is of type $\\mathrm{SL}_2, \\mathrm{GL}_2, \\mathrm{PSL}_2$, or $\\mathrm{PGL}_2$ as in the original conjecture, and claimed to provide a $3$-manifold group which violated all four variants of the conjecture. We have discovered a flaw in the work, such that the existing proof is valid only for $\\mathrm{SL}_2$ and $\\mathrm{GL}_2$. Here, we provide a modified argument for the $\\mathrm{PSL}_2$ and $\\mathrm{PGL}_2$ cases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00142",
  "author_total": 1,
  "authors": [
    {
      "name": "Montek Singh Gill"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dqc89110f7wde.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00142",
  "fulltext_url": null,
  "id": "dqc89110f7wde",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00142",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00142",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dqc89110f7wde.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00142",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00142"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Erratum to \"Linear representations of 3-manifold groups over rings\"",
  "title_text": "Erratum to \"Linear representations of 3-manifold groups over rings\"",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/dqc89110f7wde",
  "venue": "arXiv",
  "versions": []
}