{
  "id": "1709.01785",
  "version": "v1",
  "published": "2017-09-06T11:51:54.000Z",
  "updated": "2017-09-06T11:51:54.000Z",
  "title": "Non-hyperbolic solutions to tangle equations involving composite links",
  "authors": [
    "Jingling Yang"
  ],
  "comment": "40 pages, 48 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Solving tangle equations is deeply connected with studying enzyme action on DNA. The main goal of this paper is to solve the system of tangle equations $N(O+X_1)=b_1$ and $N(O+X_2)=b_2 \\# b_3$, where $X_1$ and $X_2$ are rational tangles, and $b_i$ is a 2-bridge link, for $i=1,2,3$, with $b_2$ and $b_3$ nontrivial. We solve this system of equations under the assumption $\\widetilde{O}$, the double branched cover of $O$, is not hyperbolic, i.e.$O$ is not $\\pi$-hyperbolic. Besides, we also deal with tangle equations involving 2-bridge links only under the assumption $O$ is an algebraic tangle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-06T11:51:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "composite links",
      "non-hyperbolic solutions",
      "solving tangle equations",
      "assumption",
      "studying enzyme action"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}