{
  "id": "1105.0825",
  "version": "v2",
  "published": "2011-05-04T13:45:32.000Z",
  "updated": "2011-10-06T13:08:22.000Z",
  "title": "\\int_x^{hx}(g^*α-α)",
  "authors": [
    "Światosław R. Gal",
    "Jarek Kędra"
  ],
  "categories": [
    "math.GT",
    "math.DS",
    "math.GR"
  ],
  "abstract": "Let X be a connected topological space admitting a universal cover. Let a be a degree one cohomology class on X. We define and study a two-cocycle on a group acting on X by homeomorphisms preserving the class a. We use this cocycle to investigate group actions on X. For example, we show that if an action preserves a Borel probability measure on X then the cocycle is cohomologically trivial. Under various assumptions on a homeomorphism g, we prove that it is undistorted in Homeo(X,a). In particular, we introduce a local rotation number of a homeomorphism and prove that a homeomorphism with non-constant local rotation number is undistorted.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-10-06T13:08:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-constant local rotation number",
      "homeomorphism",
      "borel probability measure",
      "group actions",
      "action preserves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.0825G"
    }
  }
}