{
  "id": "1308.6105",
  "version": "v1",
  "published": "2013-08-28T09:27:01.000Z",
  "updated": "2013-08-28T09:27:01.000Z",
  "title": "On the algebraic unknotting number",
  "authors": [
    "Maciej Borodzik",
    "Stefan Friedl"
  ],
  "comment": "32 pages, 18 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "The algebraic unknotting number u_a(K) of a knot K was introduced by Hitoshi Murakami. It equals the minimal number of crossing changes needed to turn K into an Alexander polynomial one knot. In a previous paper the authors used the Blanchfield form of a knot K to define an invariant n(K) and proved that n(K) is a lower bound on u_a(K). They also showed that n(K) subsumes all previous classical lower bounds on the (algebraic) unknotting number. In this paper we prove that n(K)=u_a(K).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-28T09:27:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "algebraic unknotting number",
      "hitoshi murakami",
      "classical lower bounds",
      "blanchfield form",
      "minimal number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.6105B"
    }
  }
}