{
  "id": "math/0407285",
  "version": "v2",
  "published": "2004-07-16T17:56:50.000Z",
  "updated": "2004-08-05T01:05:41.000Z",
  "title": "Complexes of Nonseparating Curves and Mapping Class Groups",
  "authors": [
    "Elmas Irmak"
  ],
  "comment": "24 pages, 13 figures; The result about automorphism group of complex of nonseparating curves has been extended to compact, connected, orientable surfaces of genus at least two",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $R$ be a compact, connected, orientable surface of genus $g$, $Mod_R^*$ be the extended mapping class group of $R$, $\\mathcal{C}(R)$ be the complex of curves on $R$, and $\\mathcal{N}(R)$ be the complex of nonseparating curves on $R$. We prove that if $g \\geq 2$ and $R$ has at most $g-1$ boundary components, then a simplicial map $\\lambda: \\mathcal{N}(R) \\to \\mathcal{N}(R)$ is superinjective if and only if it is induced by a homeomorphism of $R$. We prove that if $g \\geq 2$ and $R$ is not a closed surface of genus two then $Aut(\\mathcal{N}(R))= Mod_R^*$, and if $R$ is a closed surface of genus two then $Aut(\\mathcal{N}(R))= Mod_R ^* /\\mathcal{C}(Mod_R^*)$. We also prove that if $g=2$ and $R$ has at most one boundary component, then a simplicial map $\\lambda: \\mathcal{C}(R) \\to \\mathcal{C}(R)$ is superinjective if and only if it is induced by a homeomorphism of $R$. As a corollary we prove some new results about injective homomorphisms from finite index subgroups to $Mod_R^*$. The last two results complete the author's previous results to connected orientable surfaces of genus at least two.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-08-05T01:05:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99",
      "20F38"
    ],
    "keywords": [
      "nonseparating curves",
      "boundary component",
      "simplicial map",
      "orientable surface",
      "closed surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......7285I"
    }
  }
}