{
  "id": "math/0204220",
  "version": "v1",
  "published": "2002-04-17T14:45:18.000Z",
  "updated": "2002-04-17T14:45:18.000Z",
  "title": "Group cohomology and $L^p$-cohomology of finitely generated groups",
  "authors": [
    "Michael Puls"
  ],
  "comment": "Accepted Canadian Mathematical Bulletin",
  "categories": [
    "math.FA",
    "math.GR"
  ],
  "abstract": "Let $G$ be a finitely generated, infinite group, let $p>1$, and let $L^p(G)$ denote the Banach space $\\{\\sum_{x\\in G} a_xx \\mid \\sum_{x\\in G} |a_x |^p < \\infty \\}$. In this paper we will study the first cohomology group of $G$ with coefficients in $L^p(G)$, and the first reduced $L^p$-cohomology space of $G$. Most of our results will be for a class of groups that contains all finitely generated, infinite nilpotent groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-04-17T14:45:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A15",
      "20F65"
    ],
    "keywords": [
      "finitely generated groups",
      "group cohomology",
      "infinite nilpotent groups",
      "first cohomology group",
      "banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......4220P"
    }
  }
}