{
  "id": "2006.03085",
  "version": "v1",
  "published": "2020-06-04T18:13:14.000Z",
  "updated": "2020-06-04T18:13:14.000Z",
  "title": "Hierarchical hyperbolicity of graph products",
  "authors": [
    "Daniel Berlyne",
    "Jacob Russell"
  ],
  "comment": "63 pages, 12 figures. Comments welcome",
  "categories": [
    "math.GR"
  ],
  "abstract": "We show that any graph product of finitely generated groups is hierarchically hyperbolic relative to its vertex groups. We apply this result to answer two questions of Behrstock, Hagen, and Sisto: we show that the syllable metric on any graph product forms a hierarchically hyperbolic space, and that graph products of hierarchically hyperbolic groups are themselves hierarchically hyperbolic groups. This last result is a strengthening of a result of Berlai and Robbio by removing the need for extra hypotheses on the vertex groups. We also answer two questions of Genevois about the geometry of the electrification of a graph product of finite groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-04T18:13:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F67",
      "20F55"
    ],
    "keywords": [
      "hierarchical hyperbolicity",
      "hierarchically hyperbolic groups",
      "vertex groups",
      "graph product forms",
      "hierarchically hyperbolic space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 63,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}