{
  "id": "0709.2941",
  "version": "v3",
  "published": "2007-09-19T01:06:17.000Z",
  "updated": "2008-04-03T17:53:48.000Z",
  "title": "The p-harmonic boundary for finitely generated groups and the first reduced \\ell_p-cohomology",
  "authors": [
    "Michael Puls"
  ],
  "comment": "In the original paper the integers provide a counter example to Proposition 3.3. The reason is that I gave an incorrect definition for $p$-harmonic boundary. The new version has the correct defintion and some smaller changes",
  "categories": [
    "math.FA",
    "math.GR"
  ],
  "abstract": "Let $p$ be a real number greater than one and let $G$ be a finitely generated, infinite group. In this paper we introduce the $p$-harmonic boundary of $G$. We then characterize the vanishing of the first reduced $\\ell^p$-cohomology of $G$ in terms of the cardinality of this boundary. Some properties of $p$-harmonic boundaries that are preserved under rough isometries are also given. We also study the relationship between translation invariant linear functionals on a certain difference space of functions on $G$, the $p$-harmonic boundary of $G$ and the first reduced $\\ell^p$-cohomology of $G$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-04-03T17:53:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A15",
      "20F65",
      "31C20",
      "60J50"
    ],
    "keywords": [
      "finitely generated groups",
      "p-harmonic boundary",
      "translation invariant linear functionals",
      "real number greater"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.2941P"
    }
  }
}