{
  "id": "1305.2757",
  "version": "v4",
  "published": "2013-05-13T12:31:21.000Z",
  "updated": "2014-05-30T17:57:14.000Z",
  "title": "On the autonomous metric on groups of Hamiltonian diffeomorphisms of closed hyperbolic surfaces",
  "authors": [
    "Michael Brandenbursky"
  ],
  "comment": "Now it is a part of arXiv:1405.7931",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "Let $\\Sigma_g$ be a closed hyperbolic surface of genus $g$ and let $Ham(\\Sigma_g)$ be the group of Hamiltonian diffeomorphisms of $\\Sigma_g$. The most natural word metric on this group is the autonomous metric. It has many interesting properties, most important of which is the bi-invariance of this metric. In this work we show that $Ham(\\Sigma_g)$ is unbounded with respect to this metric.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-05-30T17:57:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "closed hyperbolic surface",
      "hamiltonian diffeomorphisms",
      "autonomous metric",
      "natural word metric",
      "interesting properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.2757B"
    }
  }
}