{
  "id": "2303.09852",
  "version": "v1",
  "published": "2023-03-17T09:19:07.000Z",
  "updated": "2023-03-17T09:19:07.000Z",
  "title": "Rationality of the Gromov Boundary of Hyperbolic Groups",
  "authors": [
    "Davide Perego"
  ],
  "comment": "43 pages",
  "categories": [
    "math.GR",
    "math.MG"
  ],
  "abstract": "In [BBM21], Belk, Bleak and Matucci proved that hyperbolic groups can be seen as subgroups of the rational group. In order to do so, they associated a tree of atoms to each hyperbolic group. Not so many connections between this tree and the literature on hyperbolic groups were known. In this paper, we prove an atom-version of the fellow traveler property and exponential divergence, together with other similar results. These leads to several consequences: a bound from above of the topological dimension of the Gromov boundary, the definition of an augmented tree which is quasi-isometric to the Cayley graph and a synchronous recognizer which described the equivalence relation given by the quotient map defined from the end of the tree onto the Gromov boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-17T09:19:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F67",
      "51F99",
      "68Q70"
    ],
    "keywords": [
      "hyperbolic group",
      "gromov boundary",
      "rationality",
      "fellow traveler property",
      "quotient map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}