{
  "id": "1712.05635",
  "version": "v1",
  "published": "2017-12-15T12:08:20.000Z",
  "updated": "2017-12-15T12:08:20.000Z",
  "title": "On wrapping number, adequacy and the crossing number of satellite knots",
  "authors": [
    "Adrián Jiménez Pascual"
  ],
  "comment": "28 pages, 31 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this work we establish the tightest lower bound up-to-date for the minimal crossing number of a satellite knot based on the minimal crossing number of the companion used to build the satellite. If $M$ is the wrapping number of the pattern knot, we essentially show that $c(Sat(P,C))>\\frac{M^2}{2}c(C)$. The existence of this bound will be proven when the companion knot is adequate, and it will be further tuned in the case of the companion being alternating.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-15T12:08:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "satellite knot",
      "wrapping number",
      "minimal crossing number",
      "tightest lower bound up-to-date",
      "companion knot"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}