{
  "id": "math/0311407",
  "version": "v2",
  "published": "2003-11-23T18:44:23.000Z",
  "updated": "2003-12-29T19:44:40.000Z",
  "title": "Superinjective Simplicial Maps of Complexes of Curves and Injective Homomorphisms of Subgroups of Mapping Class Groups II",
  "authors": [
    "Elmas Irmak"
  ],
  "comment": "37 pages, 19 figures; The proof for surfaces of genus two with at least two boundary components is added",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let R be a compact, connected, orientable surface of genus g with p boundary components. Let C(R) be the complex of curves on R and Mod_R^* be the extended mapping class group of R. Suppose that either g = 2 and p > 1 or g > 2 and p >= 0. We prove that a simplicial map lambda from C(R) to C(R) is superinjective if and only if it is induced by a homeomorphism of R. As a corollary, we prove that if K is a finite index subgroup of Mod_R^* and f is an injective homomorphism from K to Mod_R^*, then f is induced by a homeomorphism of R and f has a unique extension to an automorphism of Mod_R^*. This extends the author's previous results about closed connected orientable surfaces of genus at least 3, to the surface R.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-12-29T19:44:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99",
      "20F38"
    ],
    "keywords": [
      "superinjective simplicial maps",
      "injective homomorphism",
      "orientable surface",
      "simplicial map lambda",
      "finite index subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11407I"
    }
  }
}