{
  "id": "1003.1562",
  "version": "v1",
  "published": "2010-03-08T07:40:51.000Z",
  "updated": "2010-03-08T07:40:51.000Z",
  "title": "Efficient subdivision in hyperbolic groups and applications",
  "authors": [
    "Uri Bader",
    "Alex Furman",
    "Roman Sauer"
  ],
  "comment": "24 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We identify the images of the comparision maps from ordinary homology and Sobolev homology, respectively, to the $l^1$-homology of a word-hyperbolic group with coefficients in complete normed modules. The underlying idea is that there is a subdivision procedure for singular chains in negatively curved spaces that is much more efficient (in terms of the $l^1$-norm) than barycentric subdivision. The results of this paper are an important ingredient in a forthcoming proof of the authors that hyperbolic lattices in dimension at least 3 are rigid with respect to integrable measure equivalence. Moreover, we prove a proportionality principle for the simplicial volume of negatively curved manifolds with regard to integrable measure equivalence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-08T07:40:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F67",
      "55N99"
    ],
    "keywords": [
      "hyperbolic groups",
      "efficient subdivision",
      "integrable measure equivalence",
      "applications",
      "complete normed modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.1562B"
    }
  }
}