{
  "id": "0909.2421",
  "version": "v1",
  "published": "2009-09-13T15:27:47.000Z",
  "updated": "2009-09-13T15:27:47.000Z",
  "title": "Connected components of representation spaces of non-orientable surfaces",
  "authors": [
    "Frederic Palesi"
  ],
  "comment": "18 pages, 1 figure",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let M be a compact closed non-orientable surface. We show that the space of representations of the fundamental group of M into PSL(2,R) has exactly two connected components. These two components are the preimages of a certain Stiefel-Whitney characteristic class, computed in a similar way as the Euler class in the orientable case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-13T15:27:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M05",
      "57R20"
    ],
    "keywords": [
      "connected components",
      "representation spaces",
      "stiefel-whitney characteristic class",
      "fundamental group",
      "compact closed non-orientable surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.2421P"
    }
  }
}