{
  "id": "0707.0906",
  "version": "v3",
  "published": "2007-07-06T19:46:13.000Z",
  "updated": "2009-02-09T16:48:17.000Z",
  "title": "A spectral sequence to compute L2-Betti numbers of groups and groupoids",
  "authors": [
    "Roman Sauer",
    "Andreas Thom"
  ],
  "comment": "added remark 4.9 about applying spectral sequence in a non-ergodic situation; minor corrections",
  "doi": "10.1112/jlms/jdq017",
  "categories": [
    "math.DS",
    "math.AT"
  ],
  "abstract": "We construct a spectral sequence for L2-type cohomology groups of discrete measured groupoids. Based on the spectral sequence, we prove the Hopf-Singer conjecture for aspherical manifolds with poly-surface fundamental groups. More generally, we obtain a permanence result for the Hopf-Singer conjecture under taking fiber bundles whose base space is an aspherical manifold with poly-surface fundamental group. As further sample applications of the spectral sequence, we obtain new vanishing theorems and explicit computations of L2-Betti numbers of groups and manifolds and obstructions to the existence of normal subrelations in measured equivalence relations.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-02-09T16:48:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A20",
      "46L99"
    ],
    "keywords": [
      "spectral sequence",
      "l2-betti numbers",
      "poly-surface fundamental group",
      "hopf-singer conjecture",
      "l2-type cohomology groups"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.0906S"
    }
  }
}