{
  "id": "1003.4541",
  "version": "v1",
  "published": "2010-03-23T21:53:33.000Z",
  "updated": "2010-03-23T21:53:33.000Z",
  "title": "Deformation spaces of Kleinian surface groups are not locally connected",
  "authors": [
    "Aaron D. Magid"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "For any closed surface $S$ of genus $g \\geq 2$, we show that the deformation space of marked hyperbolic 3-manifolds homotopy equivalent to $S$, $AH(S \\times I)$, is not locally connected. This proves a conjecture of Bromberg who recently proved that the space of Kleinian punctured torus groups is not locally connected. Playing an essential role in our proof is a new version of the filling theorem that is based on the theory of cone-manifold deformations developed by Hodgson, Kerckhoff, and Bromberg.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-23T21:53:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "30F40"
    ],
    "keywords": [
      "kleinian surface groups",
      "deformation space",
      "kleinian punctured torus groups",
      "cone-manifold deformations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.4541M"
    }
  }
}