{
  "id": "1601.01015",
  "version": "v1",
  "published": "2016-01-05T23:10:39.000Z",
  "updated": "2016-01-05T23:10:39.000Z",
  "title": "Hidden Symmetries and Commensurability of 2-Bridge Link Complements",
  "authors": [
    "Christian Millichap",
    "William Worden"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper, we show that any non-arithmetic hyperbolic $2$-bridge link complement admits no hidden symmetries. As a corollary, we conclude that a hyperbolic $2$-bridge link complement cannot irregularly cover a hyperbolic $3$-manifold. By combining this corollary with the work of Boileau and Weidmann, we obtain a characterization of $3$-manifolds with non-trivial JSJ-decomposition and rank two fundamental groups. We also show that the only commensurable hyperbolic $2$-bridge link complements are the figure-eight knot complement and the $6_{2}^{2}$ link complement. Our work requires a careful analysis of the tilings of $\\mathbb{R}^{2}$ that come from lifting the canonical triangulations of the cusps of hyperbolic $2$-bridge link complements.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-05T23:10:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50"
    ],
    "keywords": [
      "hidden symmetries",
      "bridge link complement admits",
      "commensurability",
      "figure-eight knot complement",
      "fundamental groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}