{
  "id": "0906.3943",
  "version": "v1",
  "published": "2009-06-22T08:01:59.000Z",
  "updated": "2009-06-22T08:01:59.000Z",
  "title": "A partial order on the set of prime knots with up to 11 crossings",
  "authors": [
    "Keiichi Horie",
    "Teruaki Kitano",
    "Mineko Matsumoto",
    "Masaaki Suzuki"
  ],
  "comment": "26 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $K$ be a prime knot in $S^3$ and $G(K)=\\pi_1(S^3-K)$ the knot group. We write $K_1 \\geq K_2$ if there exists a surjective homomorphism from $G(K_1)$ onto $G(K_2)$. In this paper, we determine this partial order on the set of prime knots with up to 11 crossings. There exist such 801 prime knots and then $640,800$ should be considered. The existence of a surjective homomorphism can be proved by constructing it explicitly. On the other hand, the non-existence of a surjective homomorphism can be proved by the Alexander polynomial and the twisted Alexander polynomial. This work is an extension of the result of \\cite{KS1}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-06-22T08:01:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "prime knot",
      "partial order",
      "surjective homomorphism",
      "knot group",
      "twisted alexander polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.3943H"
    }
  }
}