{
  "id": "math/0512099",
  "version": "v1",
  "published": "2005-12-05T13:59:42.000Z",
  "updated": "2005-12-05T13:59:42.000Z",
  "title": "Inequivalent surface-knots with the same knot quandle",
  "authors": [
    "Kokoro Tanaka"
  ],
  "comment": "9 pages, no figure",
  "categories": [
    "math.GT"
  ],
  "abstract": "We have a knot quandle and a fundamental class as invariants for a surface-knot. These invariants can be defined for a classical knot in a similar way, and it is known that the pair of them is a complete invariant for classical knots. In this paper, we compare a situation in surface-knot theory with that in classical knot theory, and prove the following: There exist arbitrarily many inequivalent surface-knots of genus $g$ with the same knot quandle, and there exist two inequivalent surface-knots of genus $g$ with the same knot quandle and with the same fundamental class.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-12-05T13:59:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q45",
      "57M25"
    ],
    "keywords": [
      "knot quandle",
      "inequivalent surface-knots",
      "fundamental class",
      "classical knot theory",
      "similar way"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12099T"
    }
  }
}