{
  "id": "1905.04915",
  "version": "v1",
  "published": "2019-05-13T08:55:45.000Z",
  "updated": "2019-05-13T08:55:45.000Z",
  "title": "Alexander polynomials of simple-ribbon knots",
  "authors": [
    "Kengo Kishimoto",
    "Tetsuo Shibuya",
    "Tatsuya Tsukamoto",
    "Tsuneo Ishikawa"
  ],
  "comment": "14 pages, 10 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In a previous paper, we introduced special types of fusions, so called simple-ribbon fusions on links. A knot obtained from the trivial knot by a finite sequence of simple-ribbon fusions is called a simple-ribbon knot. Every ribbon knot with <10 crossings is a simple-ribbon knot. In this paper, we give a formula for the Alexander polynomials of simple-ribbon knots. Using the formula, we determine if a knot with 10 crossings is a simple-ribbon knot. Every simple-ribbon fusion can be realized by ``elementary\" simple-ribbon fusions. We call a knot a p-simple-ribbon knot if the knot is obtained from the trivial knot by a finite sequence of elementary p-simple-ribbon fusions for a fixed positive integer p. We provide a condition for a simple-ribbon knot to be both of an m-simple-ribbon knot and an n-simple-ribbon knot for positive integers m and n.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-13T08:55:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "alexander polynomials",
      "trivial knot",
      "finite sequence",
      "elementary p-simple-ribbon fusions",
      "positive integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}