{
  "id": "1903.04828",
  "version": "v1",
  "published": "2019-03-12T10:38:13.000Z",
  "updated": "2019-03-12T10:38:13.000Z",
  "title": "Volume versus rank of lattices in Lie groups",
  "authors": [
    "Tsachik Gelander",
    "Raz Slutsky"
  ],
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We prove that the rank (that is, the minimal size of a generating set) of lattices in a general connected Lie group is bounded by the co-volume of the projection of the lattice to the semi-simple part of the group. This is a generalization of a result by Gelander for semi-simple Lie groups and a result of Mostow for solvable Lie groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-12T10:38:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E40"
    ],
    "keywords": [
      "semi-simple lie groups",
      "general connected lie group",
      "solvable lie groups",
      "semi-simple part",
      "projection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}