{
  "id": "2209.01692",
  "version": "v1",
  "published": "2022-09-04T20:54:58.000Z",
  "updated": "2022-09-04T20:54:58.000Z",
  "title": "A note on the integrality of volumes of representations",
  "authors": [
    "Sungwoon Kim"
  ],
  "comment": "12 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $\\Gamma$ be a torsion-free, non-uniform lattice in $\\mathrm{SO}(2n,1)$. We present an elementary, combinatorial-geometrical proof of a theorem of Bucher, Burger, and Iozzi which states that the volume of a representation $\\rho:\\Gamma\\to\\mathrm{SO}(2n,1)$, properly normalized, is an integer if $n$ is greater than or equal to $2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-04T20:54:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C24",
      "22E40"
    ],
    "keywords": [
      "representation",
      "integrality",
      "non-uniform lattice",
      "elementary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}