{
  "id": "1711.04578",
  "version": "v1",
  "published": "2017-11-13T13:39:09.000Z",
  "updated": "2017-11-13T13:39:09.000Z",
  "title": "Taut foliations, contact structures and left-orderable groups",
  "authors": [
    "Steven Boyer",
    "Ying Hu"
  ],
  "comment": "34 pages, 6 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We study the left-orderability of the fundamental groups of cyclic branched covers of links which admit co-oriented taut foliations. In particular we do this for cyclic branched covers of fibered knots in integer homology $3$-spheres and cyclic branched covers of closed braids. The latter allows us to complete the proof of the L-space conjecture for closed, connected, orientable, irreducible $3$-manifolds containing a genus $1$ fibered knot. We also prove that the universal abelian cover of a manifold obtained by generic Dehn surgery on a hyperbolic fibered knot in an integer homology $3$-sphere admits a co-oriented taut foliation and has left-orderable fundamental group, even if the surgered manifold does not, and that the same holds for many branched covers of satellite knots with braided patterns.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-13T13:39:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M50",
      "57R30",
      "57M99",
      "20F60",
      "20F36"
    ],
    "keywords": [
      "cyclic branched covers",
      "contact structures",
      "left-orderable groups",
      "fibered knot",
      "fundamental group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}