{
  "id": "1608.00019",
  "version": "v1",
  "published": "2016-07-29T20:18:18.000Z",
  "updated": "2016-07-29T20:18:18.000Z",
  "title": "Natural properties of the trunk of a knot",
  "authors": [
    "Derek Davies",
    "Alexander Zupan"
  ],
  "comment": "9 pages, 3 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "The trunk of a knot in $S^3$, defined by Makoto Ozawa, is a measure of geometric complexity similar to the bridge number or width of a knot. We prove that for any two knots $K_1$ and $K_2$, we have $tr(K_1 \\# K_2) = \\max\\{tr(K_1),tr(K_2)\\}$, confirming a conjecture of Ozawa. Another conjecture of Ozawa asserts that any width-minimizing embedding of a knot $K$ also minimizes the trunk of $K$. We produce several families of probable counterexamples to this conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-29T20:18:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "natural properties",
      "conjecture",
      "geometric complexity similar",
      "ozawa asserts",
      "bridge number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}