{
  "id": "1012.4131",
  "version": "v2",
  "published": "2010-12-18T23:52:55.000Z",
  "updated": "2010-12-24T14:23:40.000Z",
  "title": "Unknotting number and number of Reidemeister moves needed for unlinking",
  "authors": [
    "Chuichiro Hayashi",
    "Miwa Hayashi"
  ],
  "comment": "10pages, 8 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Using unknotting number, we introduce a link diagram invariant of Hass and Nowik type, which changes at most by 2 under a Reidemeister move. As an application, we show that a certain infinite sequence of diagrams of the trivial two-component link need quadratic number of Reidemeister moves for being unknotted with respect to the number of crossings. Assuming a certain conjecture on unknotting numbers of a certain series of composites of torus knots, we show that the above diagrams need quadratic number of Reidemeister moves for being splitted.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-12-24T14:23:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "unknotting number",
      "reidemeister moves",
      "two-component link need quadratic number",
      "trivial two-component link need quadratic",
      "diagrams need quadratic number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.4131H"
    }
  }
}