{
  "id": "1301.0665",
  "version": "v2",
  "published": "2013-01-04T03:38:21.000Z",
  "updated": "2013-03-12T21:06:13.000Z",
  "title": "On left-orderable fundamental groups and Dehn surgeries on twist knots",
  "authors": [
    "Anh T. Tran"
  ],
  "comment": "This paper has been withdrawn by the author. This paper now becomes a part of the paper arXiv:1301.2637",
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that the resulting manifold by $r$-surgery on the hyperbolic twist knot $K_m, \\, m \\ge 2$, has left-orderable fundamental group if the slope $r$ satisfies the condition $r \\in (-4,2m)$ if $m$ is even, and $r \\in [0,4] \\cup (\\frac{4m}{\\omega}+4, 2m+4)$ if $m$ is odd, where $\\omega>1$ is the unique real solution of the equation $x e^{x}=4m$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-12T21:06:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "left-orderable fundamental group",
      "dehn surgeries",
      "hyperbolic twist knot",
      "unique real solution",
      "resulting manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.0665T"
    }
  }
}