{
  "id": "0905.0008",
  "version": "v4",
  "published": "2009-05-01T12:41:10.000Z",
  "updated": "2009-12-27T14:55:15.000Z",
  "title": "The warping degree of a link diagram",
  "authors": [
    "Ayaka Shimizu"
  ],
  "comment": "28 pages, 16 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "For an oriented link diagram D, the warping degree d(D) is the smallest number of crossing changes which are needed to obtain a monotone diagram from D. We show that d(D)+d(-D)+sr(D) is less than or equal to the crossing number of D, where -D denotes the inverse of D and sr(D) denotes the number of components which have at least one self-crossing. Moreover, we give a necessary and sufficient condition for the equality. We also consider the minimal d(D)+d(-D)+sr(D) for all diagrams D. For the warping degree and linking warping degree, we show some relations to the linking number, unknotting number, and the splitting number.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-12-27T14:55:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "warping degree",
      "oriented link diagram",
      "monotone diagram",
      "sufficient condition",
      "smallest number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.0008S"
    }
  }
}