{
  "id": "math/0405028",
  "version": "v2",
  "published": "2004-05-03T13:06:04.000Z",
  "updated": "2007-11-14T17:34:51.000Z",
  "title": "Constructing equivariant maps for representations",
  "authors": [
    "S. Francaviglia"
  ],
  "comment": "Changes from V1: The paper has been substantially reorganised. New applications added. This is the version accepted for pubblication. To appear on Ann. Inst. Fourier",
  "categories": [
    "math.GT",
    "math.DS"
  ],
  "abstract": "We show that if G is a discrete subgroup of the group of the isometries of the hyperbolic k-space H^k, and if R is a representation of G into the group of the isometries of H^n, then any R-equivariant map F from H^k to H^n extends to the boundary in a weak sense in the setting of Borel measures. As a consequence of this fact, we obtain an extension of a result of Besson, Courtois and Gallot about the existence of volume non-increasing, equivariant maps. Moreover, under an additional hypothesis, we show that the weak extension we obtain is actually a measurable R-equivariant map from the boundary of H^k to the closure of H^n. We use this fact to obtain measurable versions of Cannon-Thurston-type results for equivariant Peano curves.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-11-14T17:34:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "37A99"
    ],
    "keywords": [
      "constructing equivariant maps",
      "representation",
      "equivariant peano curves",
      "discrete subgroup",
      "isometries"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5028F"
    }
  }
}