{
  "id": "1709.05617",
  "version": "v1",
  "published": "2017-09-17T07:29:02.000Z",
  "updated": "2017-09-17T07:29:02.000Z",
  "title": "On eigenvalues of double branched covers",
  "authors": [
    "Kouki Sato"
  ],
  "comment": "13 pages, 15 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "For a given knot, we study the minimal number of positive eigenvalues of the double branched cover over spanning surfaces for the knot. The value gives a lower bound for various genera, the dealternating number and the alternation number of knots, and we prove that Batson's bound for the non-orientable 4-genus gives an estimate of the value. In addition, we use the value to give a necessary condition for being quasi-alternating.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-17T07:29:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "double branched cover",
      "eigenvalues",
      "minimal number",
      "lower bound",
      "alternation number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}