{
  "id": "1112.1465",
  "version": "v3",
  "published": "2011-12-07T03:26:49.000Z",
  "updated": "2012-06-13T19:59:33.000Z",
  "title": "On discontinuities of cocycles in cohomology theories for topological groups",
  "authors": [
    "Tim Austin"
  ],
  "comment": "42 pages, 1 figure [TDA May 1, 2012] Replaced with a substantially new argument, which also fixes some howlers in the first version. [TDA June 13, 2012] Some minor corrections and editing",
  "categories": [
    "math.GR",
    "math.GN",
    "math.KT"
  ],
  "abstract": "This paper studies Moore's measurable cohomology theory for locally compact groups and Polish modules. An elementary dimension-shifting argument is used to show that all classes in that theory have representatives with considerable extra topological structure beyond measurability. Using this, for certain target modules one can also construct a direct comparison map with a different cohomology theory for topological groups defined by Segal, and show that this map is an isomorphism.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-06-13T19:59:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20J06",
      "22D05",
      "18G10"
    ],
    "keywords": [
      "topological groups",
      "studies moores measurable cohomology theory",
      "discontinuities",
      "paper studies moores measurable cohomology",
      "direct comparison map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.1465A"
    }
  }
}