{
  "id": "1207.0451",
  "version": "v7",
  "published": "2012-07-02T17:44:34.000Z",
  "updated": "2013-04-12T15:12:46.000Z",
  "title": "Vanishing of $\\ell^p$-cohomology and transportation cost",
  "authors": [
    "Antoine Gournay"
  ],
  "comment": "13 pages. Added references, clarified some calculations",
  "categories": [
    "math.GR",
    "math.DG"
  ],
  "abstract": "In this paper, it is shown that the reduced $\\ell^p$-cohomology is trivial for a class of finitely generated amenable groups called transport amenable. These groups are those for which there exist a sequence of measures $\\xi_n$ converging to a left-invariant mean and such that the transport cost between $\\xi_n$ displaced by multiplication on the right by a fixed element and $\\xi_n$ is bounded in $n$. This class contains groups with controlled F{\\o}lner sequence (such as polycylic groups) as well as some wreath products (such as arbitrary wreath products of finitely generated Abelian groups).",
  "revisions": [
    {
      "version": "v7",
      "updated": "2013-04-12T15:12:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20J06",
      "20E22",
      "31C05",
      "43A07",
      "43A15"
    ],
    "keywords": [
      "transportation cost",
      "cohomology",
      "arbitrary wreath products",
      "class contains groups",
      "finitely generated abelian groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.0451G"
    }
  }
}