{
  "id": "math/9606216",
  "version": "v1",
  "published": "1996-06-12T00:00:00.000Z",
  "updated": "1996-06-12T00:00:00.000Z",
  "title": "The outside of the Teichmuller space of punctured tori in Maskit's embedding",
  "authors": [
    "Jouni Parkkonen"
  ],
  "categories": [
    "math.GT",
    "math.DS"
  ],
  "abstract": "We consider the following question: Which parameters in the extension of a rational pleating ray across the boundary of $\\Cal M$, the Maskit embedding of the Teichm\\\"uller space of once punctured tori correspond to a Kleinian group? Using methods of Keen and Series and Wright we prove a local result, stating that on each rational ray there is a sequence of parameters in $\\overline\\Bbb H\\setminus\\Cal M$ accumulating at the boundary point of $\\Cal M$ on the ray. These are the unique parameters on the extended $p/q$ ray for which the special word $W_{p/q}$ is a primitive elliptic M\\\"obius transformation. We also show that the discrete groups with elliptic elements in the complement of $\\overline{\\Cal M}$ are boundary groups of deformation spaces of certain Kleinian groups representing a punctured torus on their invariant component.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1996-06-12T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "punctured torus",
      "teichmuller space",
      "maskits embedding",
      "kleinian group",
      "parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}