{
  "id": "1209.3119",
  "version": "v1",
  "published": "2012-09-14T08:06:39.000Z",
  "updated": "2012-09-14T08:06:39.000Z",
  "title": "On 3-super bridge knots",
  "authors": [
    "Rama Mishra"
  ],
  "comment": "11 pages, 7 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "It is known that there are only finitely many knots with super bridge index 3. Jin and Jeon have provided a list of possible such candidates. However, they conjectured that the only knots with super bridge index 3 are trefoil and the figure eight knot. In this paper, we prove that the $5_2$ knot and the $6_2$ knot are also 3-super bridge knots by providing a polynomial representation of these knots in degree $6.$ This also answers a question asked by Durfee and O'Shea in their paper on polynomial knots: is there any 5-crossing knot in degree 6?",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-14T08:06:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "14P25"
    ],
    "keywords": [
      "bridge knots",
      "super bridge index",
      "polynomial representation",
      "polynomial knots",
      "candidates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.3119M"
    }
  }
}