{
  "abstract": "The Akutsu-Deguchi-Ohtsuki (ADO) invariants of links are a non-semisimple version of the colored Jones polynomials. We prove that the top coefficients of the ADO invariants of links in $S^3$ are multiplicative under Murasugi-sum along connected minimal genus Seifert surfaces. More generally, for any simple complex Lie algebra $\\mathfrak{g}$ of type ADE and any $r\\geq 3$, we prove that the top coefficient of the $r$-th $\\mathfrak{g}$-ADO invariant is multiplicative under Murasugi-sum. As a corollary, we get that all the $\\mathfrak{g}$-ADO invariants of fibred links are $q$-monic, generalizing a previous result of the authors for $\\mathfrak{sl}_2$. Moreover, whenever $\\mathfrak{u}_q(\\mathfrak{g})$ is ribbon, we find an expression for the top coefficient of the $r$-th $\\mathfrak{g}$-ADO invariant in terms of Hopf algebra integrals of universal $\\mathfrak{u}_q(\\mathfrak{g})$-invariants of bottom tangles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08638",
  "author_total": 2,
  "authors": [
    {
      "name": "Daniel López Neumann"
    },
    {
      "name": "Roland van der Veen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7mp216c70d2qp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08638",
  "fulltext_url": null,
  "id": "7mp216c70d2qp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08638",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GT"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7221005270",
  "pdf_url": "https://arxiv.org/pdf/2610.08638",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7mp216c70d2qp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08638",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08638"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Top coefficients of ADO invariants are Murasugi-sum multiplicative",
  "title_text": "Top coefficients of ADO invariants are Murasugi-sum multiplicative",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/7mp216c70d2qp",
  "venue": "arXiv",
  "versions": []
}