{
  "abstract": "We prove that the colored Jones polynomial of a knot does not determine the Links--Gould polynomial (associated with the 4-dimensional representation of the Lie superalgebra $\\mathfrak{sl}(2|1)$) with two different approaches: the first is to find a concrete genus 2 mutation pair with different Links--Gould polynomials, and the second follows from the fact that the colored Jones polynomial is invariant under Conway mutation whereas the colored Links--Gould polynomial is not. The first approach also applies to a related family of polynomial invariants of Kashaev--Mangazeev, which are conjectured to be the $\\mathfrak{sl}(n|1)$-knot invariants colored by the $2^n$-dimensional irreducible representation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07198",
  "author_total": 2,
  "authors": [
    {
      "name": "Stavros Garoufalidis"
    },
    {
      "name": "Shana Yunsheng Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1a0k4r6mmj5wx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07198",
  "fulltext_url": null,
  "id": "1a0k4r6mmj5wx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07198",
  "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": "W7220894914",
  "pdf_url": "https://arxiv.org/pdf/2610.07198",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1a0k4r6mmj5wx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07198",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07198"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The colored Jones polynomial does not determine the Links--Gould polynomial",
  "title_text": "The colored Jones polynomial does not determine the Links--Gould polynomial",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/1a0k4r6mmj5wx",
  "venue": "arXiv",
  "versions": []
}