{
  "id": "1803.09284",
  "version": "v3",
  "published": "2018-03-25T15:58:46.000Z",
  "updated": "2019-02-24T19:41:48.000Z",
  "title": "Quasi-isometric invariance of continuous group $L^p$-cohomology, and first applications to vanishings",
  "authors": [
    "Marc Bourdon",
    "Bertrand Remy"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We show that the continuous $L^p$-cohomology of locally compact second countable groups is a quasi-isometric invariant. As an application, we prove partial results supporting a positive answer to a question asked by M.~Gromov, suggesting a classical behaviour of continuous $L^p$-cohomology of simple real Lie groups. In addition to quasi-isometric invariance, the ingredients are a spectral sequence argument and Pansu's vanishing results for real hyperbolic spaces. In the best adapted cases of simple Lie groups, we obtain nearly half of the relevant vanishings.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2019-02-24T19:41:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20J05",
      "20J06",
      "22E15",
      "22E41",
      "53C35",
      "55B35",
      "57T10",
      "57T15"
    ],
    "keywords": [
      "quasi-isometric invariance",
      "first applications",
      "continuous group",
      "cohomology",
      "simple real lie groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}