{
  "id": "0808.2087",
  "version": "v1",
  "published": "2008-08-15T03:45:27.000Z",
  "updated": "2008-08-15T03:45:27.000Z",
  "title": "Connectivity Properties of Horospheres in Euclidean Buildings and Applications to Finiteness Properties of Discrete Groups",
  "authors": [
    "Kai-Uwe Bux",
    "Kevin Wortman"
  ],
  "comment": "27 pages",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "Let G(O_S) be an S-arithmetic subgroup of a connected, absolutely almost simple linear algebraic group G over a global function field K. We show that the sum of local ranks of G determines the homological finiteness properties of G(O_S) provided the K-rank of G is 1. This shows that the general upper bound for the finiteness length of G(O_S) established in an earlier paper is sharp in this case. The geometric analysis underlying our result determines the conectivity properties of horospheres in thick Euclidean buildings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-08-15T03:45:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G30",
      "20E42",
      "20F65"
    ],
    "keywords": [
      "finiteness properties",
      "discrete groups",
      "connectivity properties",
      "horospheres",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.2087B"
    }
  }
}