{
  "id": "1502.01450",
  "version": "v1",
  "published": "2015-02-05T08:11:32.000Z",
  "updated": "2015-02-05T08:11:32.000Z",
  "title": "Computations of quandle cocyle invariants of surface-links using marked graph diagrams",
  "authors": [
    "Seiichi Kamada",
    "Jieon Kim",
    "Sang Youl Lee"
  ],
  "comment": "40 pages, 29 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "By using the cohomology theory of quandles, quandle cocycle invariants and shadow quandle cocycle invariants are defined for oriented links and surface-links via broken surface diagrams. By using symmetric quandles, symmetric quandle cocycle invariants are also defined for unoriented links and surface-links via broken surface diagrams. A marked graph diagram is a link diagram possibly with $4$-valent vertices equipped with markers. S. J. Lomonaco, Jr. and K. Yoshikawa introduced a method of describing surface-links by using marked graph diagrams. In this paper, we give interpretations of these quandle cocycle invariants in terms of marked graph diagrams, and introduce a method of computing them from marked graph diagrams.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-05T08:11:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q45",
      "57M25"
    ],
    "keywords": [
      "marked graph diagram",
      "quandle cocyle invariants",
      "surface-links",
      "broken surface diagrams",
      "shadow quandle cocycle invariants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150201450K"
    }
  }
}