{
  "id": "1002.5040",
  "version": "v2",
  "published": "2010-02-26T19:02:01.000Z",
  "updated": "2010-02-26T23:12:42.000Z",
  "title": "A cohomological characterisation of Yu's Property A for metric spaces",
  "authors": [
    "J. Brodzki",
    "G. A. Niblo",
    "N. J. Wright"
  ],
  "categories": [
    "math.GT",
    "math.KT"
  ],
  "abstract": "Property A was introduced by Yu as a non-equivariant analogue of amenability. Nigel Higson posed the question of whether there is a homological characterisation of property A. In this paper we answer Higson's question affirmatively by constructing analogues of group cohomology and bounded cohomology for a metric space X, and show that property A is equivalent to vanishing cohomology. Using these cohomology theories we also give a characterisation of property A in terms of the existence of an asymptotically invariant mean on the space.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-02-26T23:12:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "metric space",
      "yus property",
      "cohomological characterisation",
      "answer higsons question",
      "cohomology theories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.5040B"
    }
  }
}