{
  "id": "1412.3168",
  "version": "v1",
  "published": "2014-12-10T01:05:39.000Z",
  "updated": "2014-12-10T01:05:39.000Z",
  "title": "Some minimal elements for a partial order of prime knots",
  "authors": [
    "Teruaki Kitano",
    "Masaaki Suzuki"
  ],
  "comment": "3 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "A partial order on the set of prime knots can be defined by the existence of an epimorphism between knot groups. We prove that all the prime knots with up to $6$ crossings are minimal. We also show that each fibered knot with the irreducible Alexander polynomial is minimal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-10T01:05:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "prime knots",
      "partial order",
      "minimal elements",
      "knot groups",
      "irreducible alexander polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.3168K"
    }
  }
}