{
  "id": "1610.09987",
  "version": "v1",
  "published": "2016-10-31T15:55:46.000Z",
  "updated": "2016-10-31T15:55:46.000Z",
  "title": "Conditions of smoothness of moduli spaces of flat connections and of representation varieties",
  "authors": [
    "Nan-Kuo Ho",
    "Graeme Wilkin",
    "Siye Wu"
  ],
  "comment": "14 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We use gauge theoretic and algebraic methods to reexamine the sufficient conditions for smooth points on the moduli space of flat connections on a compact manifold and on the representation variety of a finitely generated and presented group. In particular, we give a complete proof of the slice theorem for the action of the group of gauge transformations on the space of flat connections. We show that on a compact non-orientable surface, flat connections with minimal isotropy need not descend to smooth points on the moduli space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-31T15:55:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58D27",
      "57M05",
      "20F05"
    ],
    "keywords": [
      "flat connections",
      "moduli space",
      "representation variety",
      "smoothness",
      "smooth points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}