{
  "id": "2303.11218",
  "version": "v1",
  "published": "2023-03-20T15:49:23.000Z",
  "updated": "2023-03-20T15:49:23.000Z",
  "title": "A note on arithmetic lattices in $\\mathbb{H}^n$ and exotic subgroups of hyperbolic groups",
  "authors": [
    "Monika Kudlinska"
  ],
  "comment": "6 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We construct the first known infinite family of quasi-isometry classes of subgroups of hyperbolic groups which are not hyperbolic and are of type $\\mathrm{FP}(\\mathbb{Q})$. We give a simple criterion for producing many non-hyperbolic subgroups of hyperbolic groups with strong finiteness properties. We also observe that local hyperbolicity and algebraic fibring are mutually exclusive in higher dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-20T15:49:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F67",
      "20E07",
      "20J05",
      "57M07"
    ],
    "keywords": [
      "hyperbolic groups",
      "exotic subgroups",
      "arithmetic lattices",
      "strong finiteness properties",
      "simple criterion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}