{
  "id": "1310.5054",
  "version": "v2",
  "published": "2013-10-18T15:18:01.000Z",
  "updated": "2013-10-22T17:34:39.000Z",
  "title": "On the degeneration of tunnel numbers under connected sum",
  "authors": [
    "Tao Li",
    "Ruifeng Qiu"
  ],
  "comment": "17 pages, 3 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that, for any integer $n\\ge 3$, there is a prime knot $k$ such that (1) $k$ is not meridionally primitive, and (2) for every $m$-bridge knot $k'$ with $m\\leq n$, the tunnel numbers satisfy $t(k\\# k')\\le t(k)$. This gives counterexamples to a conjecture of Morimoto and Moriah on tunnel number under connected sum and meridionally primitive knots.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-10-22T17:34:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N10",
      "57M25"
    ],
    "keywords": [
      "connected sum",
      "degeneration",
      "tunnel numbers satisfy",
      "prime knot",
      "bridge knot"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.5054L"
    }
  }
}