{
  "id": "1207.0624",
  "version": "v3",
  "published": "2012-07-03T09:59:45.000Z",
  "updated": "2013-02-27T19:08:18.000Z",
  "title": "On the autonomous metric on the group of area-preserving diffeomorphisms of the 2-disc",
  "authors": [
    "Michael Brandenbursky",
    "Jarek Kedra"
  ],
  "comment": "This a revised version, to appear in Algebraic and Geometric Topology, 20 pages, 1 figure",
  "categories": [
    "math.GT",
    "math.GR",
    "math.SG"
  ],
  "abstract": "Let $D^2$ be the open unit disc in the Euclidean plane and let $G:= Diff(D2; area)$ be the group of smooth compactly supported area-preserving diffeomorphisms of $D^2$. We investigate the properties of G endowed with the autonomous metric. In particular, we construct a bi-Lipschitz homomorphism $Z^k \\rightarrow G$ of a finitely generated free abelian group of an arbitrary rank. We also show that the space of homogeneous quasi-morphisms vanishing on all autonomous diffeomorphisms in the above group is infinite dimensional.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-02-27T19:08:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "autonomous metric",
      "finitely generated free abelian group",
      "open unit disc",
      "smooth compactly supported area-preserving diffeomorphisms",
      "euclidean plane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.0624B"
    }
  }
}