{
  "id": "2203.11996",
  "version": "v1",
  "published": "2022-03-22T18:49:44.000Z",
  "updated": "2022-03-22T18:49:44.000Z",
  "title": "Commensurating HNN-extensions: hierarchical hyperbolicity and biautomaticity",
  "authors": [
    "Sam Hughes",
    "Motiejus Valiunas"
  ],
  "comment": "32 pages, 4 figures. Comments are welcome!",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We construct a CAT(0) hierarchically hyperbolic group (HHG) acting geometrically on the product of a hyperbolic plane and a locally-finite tree which is not biautomatic. This gives the first example of an HHG which is not biautomatic, the first example of a non-biautomatic CAT(0) group of flat-rank 2, and the first example of an HHG which is coarsely injective but not Helly. Our proofs heavily utilise the space of geodesic currents for a hyperbolic surface.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-22T18:49:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F10",
      "57K20",
      "57M50",
      "37E30",
      "20F67"
    ],
    "keywords": [
      "hierarchical hyperbolicity",
      "commensurating hnn-extensions",
      "first example",
      "biautomaticity",
      "locally-finite tree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}