{
  "annotation_id": "efaf777c-0fa7-4fe0-8c40-b758828ebfc4",
  "date_created": "2026-02-17T05:53:08.676000Z",
  "date_modified": "2026-02-17T05:53:08.676000Z",
  "file_hash": "5830607159e2ab52d9ee407a681275f20111d5593c05e8db29fdea5d4923edce",
  "private": false,
  "record": {
    "abstract": "Given any countable group $G$, we construct uncountably many quasi-isometry classes of proper geodesic metric spaces with quasi-isometry group isomorphic to $G$. Moreover, if the group $G$ is a hyperbolic group, the spaces we construct are hyperbolic metric spaces.\n  We make use of a rigidity phenomenon for quasi-isometries exhibited by many symmetric spaces, called strong quasi-isometric rigidity. Our method involves the construction of new examples of strongly quasi-isometrically rigid spaces, arising as graphs of strongly quasi-isometrically rigid rank-one symmetric spaces.",
    "arxiv_id": "2601.06261",
    "authors": [
      "Paula Heim",
      "Joseph MacManus",
      "Lawk Mineh"
    ],
    "categories": [
      "math.GR",
      "math.MG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Realising all countable groups as quasi-isometry groups",
    "url": "https://arxiv.org/abs/2601.06261",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "894c341c-a923-4870-b055-8b664889fc03",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}