{
  "id": "2401.01536",
  "version": "v1",
  "published": "2024-01-03T04:24:43.000Z",
  "updated": "2024-01-03T04:24:43.000Z",
  "title": "The (twisted/$L^2$)-Alexander polynomial of ideally triangulated 3-manifolds",
  "authors": [
    "Stavros Garoufalidis",
    "Seokbeom Yoon"
  ],
  "comment": "16 pages, 6 figures",
  "categories": [
    "math.GT",
    "hep-th"
  ],
  "abstract": "We establish a connection between the Alexander polynomial of a knot and its twisted and $L^2$-versions with the triangulations that appear in 3-dimensional hyperbolic geometry. Specifically, we introduce twisted Neumann--Zagier matrices of ordered ideal triangulations and use them to provide formulas for the Alexander polynomial and its variants, the twisted Alexander polynomial and the $L^2$-Alexander torsion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-03T04:24:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperbolic geometry",
      "twisted neumann-zagier matrices",
      "ordered ideal triangulations",
      "twisted alexander polynomial",
      "alexander torsion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}