{
  "abstract": "Let $T(p,q;r,s)$ be the twisted torus link obtained from the torus link $T(p,q)$ by adding $s$ full twists to $r$ adjacent strands, and let $C$ be an unknotted circle encircling those strands. For all $p$, $q$, and $r$ we compute the multivariable Alexander polynomial of $T(p,q)\\cup C$ in closed form. A relation of Silver and Williams between the Alexander polynomials of a link and of its $1/n$ Dehn fillings then gives a closed formula for the multivariable Alexander polynomial of every twisted torus link $T(p,q;r,s)$, answering a question of Adnan and Park. When $\\gcd(p,q)=1$, so that $T(p,q;r,s)$ is a knot, the formula is a sum of $pr$ monomials with coefficient $+1$, divided by cyclotomic factors, and its exponents are governed by an elementary counting function on the orbit of $q$ modulo $p$. Because the numerator has no cancellation, we are able to give the degree for all $s$ and a simple non-fiberedness criterion.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03265",
  "author_total": 1,
  "authors": [
    {
      "name": "Birch Bryant"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8z3f64trxb1g4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03265",
  "fulltext_url": null,
  "id": "8z3f64trxb1g4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03265",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03265",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8z3f64trxb1g4.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03265",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03265"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Multivariable Alexander polynomials of twisted torus links via Dehn surgery",
  "title_text": "Multivariable Alexander polynomials of twisted torus links via Dehn surgery",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/8z3f64trxb1g4",
  "venue": "arXiv",
  "versions": []
}