{
  "id": "1708.03000",
  "version": "v1",
  "published": "2017-08-09T20:16:47.000Z",
  "updated": "2017-08-09T20:16:47.000Z",
  "title": "The non-orientable 4-genus for knots with 8 or 9 crossings",
  "authors": [
    "Stanislav Jabuka",
    "Tynan Kelly"
  ],
  "comment": "31 pages, 17 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "The non-orientable 4-genus of a knot in the 3-sphere is defined as the smallest first Betti number of any non-orientable surface smoothly and properly embedded in the 4-ball, with boundary the given knot. We compute the non-orientable 4-genus for all knots with crossing number 8 or 9. As applications we prove a conjecture of Murakami's and Yasuhara's, and give a new lower bound for the slicing number of knot.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-09T20:16:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "smallest first betti number",
      "lower bound",
      "slicing number",
      "crossing number",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}