{
  "id": "2312.14025",
  "version": "v1",
  "published": "2023-12-21T16:54:42.000Z",
  "updated": "2023-12-21T16:54:42.000Z",
  "title": "De Rham $L^p$-Cohomology For Higher Rank Spaces And Groups: Critical Exponents And Rigidity",
  "authors": [
    "Marc Bourdon",
    "Bertrand Rémy"
  ],
  "comment": "40 pages",
  "categories": [
    "math.GR",
    "math.DG"
  ],
  "abstract": "We initiate the investigation of critical exponents (in degree equal to the rank) for the vanishing of L^p-cohomology of higher rank Lie groups and related manifolds. We deal with the rank 2 case and exhibit such phenomena for SL$_3$(R) and for a family of 5-dimensional solvable Lie groups. This leads us to exhibit a continuum of quasi-isometry classes of rank 2 solvable Lie groups of non-positive curvature. We provide a detailed description of the $L^p$-cohomology of the real and complex hyperbolic spaces, to be combined with a spectral sequence argument for our higher-rank results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-21T16:54:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20J05",
      "20J06",
      "22E15",
      "22E41",
      "53C35",
      "55B35",
      "57T10",
      "57T15"
    ],
    "keywords": [
      "higher rank spaces",
      "critical exponents",
      "cohomology",
      "solvable lie groups",
      "higher rank lie groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}