{
  "id": "1304.0936",
  "version": "v4",
  "published": "2013-04-03T12:40:32.000Z",
  "updated": "2013-08-08T17:49:52.000Z",
  "title": "On the existence of representations of finitely presented groups in compact Lie groups",
  "authors": [
    "Kim A. Froyshov"
  ],
  "comment": "22 pages, to appear in `Topology and its Applications'. v2: The title was changed, reflecting the fact that Cor. 1.1 was already known. The old Theorem 1.5 was omitted, as it is easily proved using a result in the new appendix. v3: Only minor changes. v4: The proof of Prop. 2.1 was omitted, because the result was already known. Minor changes following referee's suggestions",
  "journal": "Topology and its Applications 160 (2013) 1987-2002",
  "categories": [
    "math.GT",
    "math.AT",
    "math.GR"
  ],
  "abstract": "Given a finite, connected 2-complex $X$ such that $b_2(X)\\le1$ we establish two existence results for representations of the fundamental group of $X$ into compact connected Lie groups $G$, with prescribed values on certain loops. If $b_2(X)=1$ we assume $G=SO(3)$ and that the cup product on the first rational cohomology group of $X$ is non-zero.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-08-08T17:49:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M07",
      "57M20"
    ],
    "keywords": [
      "compact lie groups",
      "representations",
      "first rational cohomology group",
      "compact connected lie groups",
      "fundamental group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.0936F"
    }
  }
}