{
  "id": "2110.03082",
  "version": "v3",
  "published": "2021-10-06T22:03:26.000Z",
  "updated": "2022-01-06T18:19:34.000Z",
  "title": "The Jones Polynomial from a Goeritz Matrix",
  "authors": [
    "Joe Boninger"
  ],
  "comment": "Version 3: minor correction",
  "journal": "Bull. Long. Math. Soc. 55 (2023), no. 2, 732-755",
  "doi": "10.1112/blms.12753",
  "categories": [
    "math.GT"
  ],
  "abstract": "We give an explicit algorithm for calculating the Kauffman bracket of a link diagram from a Goeritz matrix for that link. Further, we show how the Jones polynomial can be recovered from a Goeritz matrix when the corresponding checkerboard surface is orientable, or when more information is known about its Gordon-Litherland form. In the process we develop a theory of Goeritz matrices for cographic matroids, which extends the bracket polynomial to any symmetric integer matrix. We place this work in the context of links in thickened surfaces.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2022-01-06T18:19:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K14",
      "05B35"
    ],
    "keywords": [
      "goeritz matrix",
      "jones polynomial",
      "symmetric integer matrix",
      "link diagram",
      "explicit algorithm"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}