{
  "id": "2103.11079",
  "version": "v1",
  "published": "2021-03-20T02:59:02.000Z",
  "updated": "2021-03-20T02:59:02.000Z",
  "title": "On inequalities between unknotting numbers and crossing numbers of spatial embeddings of trivializable graphs and handlebody-knots",
  "authors": [
    "Yuta Akimoto"
  ],
  "comment": "18 pages, 36 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We study relations between unknotting number and crossing number of a spatial embedding of a handcuff-graph and a theta curve. It is well known that for any non-trivial knot $K$ twice the unknotting number of $K$ is less than or equal to the crossing number of $K$ minus one. We show that this is extended to handlebody-knots. We also characterize the handlebody-knots which satisfy the equality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-20T02:59:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10",
      "05C10"
    ],
    "keywords": [
      "crossing number",
      "unknotting number",
      "spatial embedding",
      "trivializable graphs",
      "handlebody-knots"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}