{
  "id": "math/0701766",
  "version": "v3",
  "published": "2007-01-26T05:09:26.000Z",
  "updated": "2007-03-13T16:11:51.000Z",
  "title": "Knots with g(E(K)) = 2 and g(E(K#K#K)) = 6 and Morimoto's Conjecture",
  "authors": [
    "Tsuyoshi Kobayashi",
    "Yo'av Rieck"
  ],
  "comment": "6 pages. Final version",
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that there exist knots K in S^3 with g(E(K))=2 and g(E(K#K#K))=6. Together with Theorem~1.5 of [1], this proves existence of counterexamples to Morimoto's Conjecture (Conjecture 1.5 of [2]). This is a special case of arxiv.org/abs/math.GT/0701765 [1] Tsuyoshi Kobayashi and Yo'av Rieck. On the growth rate of the tunnel number of knots. J. Reine Angew. Math., 592:63--78, 2006. [2] Kanji Morimoto. On the super additivity of tunnel number of knots.Math. Ann., 317(3):489--508, 2000.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-03-13T16:11:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99"
    ],
    "keywords": [
      "morimotos conjecture",
      "tunnel number",
      "kanji morimoto",
      "special case",
      "reine angew"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1766K"
    }
  }
}