{
  "id": "1311.3291",
  "version": "v3",
  "published": "2013-11-13T20:56:40.000Z",
  "updated": "2014-07-01T19:19:15.000Z",
  "title": "Left-orderability and cyclic branched coverings",
  "authors": [
    "Ying Hu"
  ],
  "comment": "13 pages, 2 figures; the abstract and introduction are substantially revised from the previous version; a mathematical typo is corrected in section 4;",
  "categories": [
    "math.GT"
  ],
  "abstract": "We provide an alternative proof of a sufficient condition for the fundamental group of the $n^{th}$ cyclic branched cover of $S^3$ along a prime knot $K$ to be left-orderable, which is originally due to Boyer-Gordon-Watson. As an application of this sufficient condition, we show that for any $(p,q)$ two-bridge knot, with $p\\equiv 3 \\text{ mod } 4$, there are only finitely many cyclic branched covers whose fundamental groups are not left-orderable. This answers a question posed by D{\\c a}bkowski, Przytycki and Togha.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-07-01T19:19:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M05",
      "57M12"
    ],
    "keywords": [
      "cyclic branched coverings",
      "left-orderability",
      "fundamental group",
      "sufficient condition",
      "two-bridge knot"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.3291H"
    }
  }
}