{
  "id": "0910.2872",
  "version": "v1",
  "published": "2009-10-15T13:33:28.000Z",
  "updated": "2009-10-15T13:33:28.000Z",
  "title": "The Goeritz matrix and signature of a two bridge knot",
  "authors": [
    "Michael Gallaspy",
    "Stanislav Jabuka"
  ],
  "comment": "22 pages, 8 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "According to a formula by Gordon and Litherland, the signature of a knot K can be computed as the signature of a Goeritz matrix of K minus a suitable correction term, read off from the diagram of K. In this article, we consider the family of two bridge knots K(p/q) and compute the signature of their Goeritz matrices in terms of the coefficients of the continued fraction expansion of p/q. In many cases we also compute the value of the correction term. We show that for every two bridge knot K(p/q), there are \"even continued fraction expansions\" of p/q, for which the correction term vanishes, thereby fully computing the signature of K(p/q). We provide an algorithm for finding even continued fraction expansions. This article is the result of an REU study conducted by the first author under the direction of the second.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-15T13:33:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57N70"
    ],
    "keywords": [
      "bridge knot",
      "goeritz matrix",
      "continued fraction expansion",
      "correction term vanishes",
      "suitable correction term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.2872G"
    }
  }
}