{
  "id": "1112.1617",
  "version": "v2",
  "published": "2011-12-07T16:35:10.000Z",
  "updated": "2012-04-04T20:52:40.000Z",
  "title": "Simplicial Maps of the Complexes of Curves on Nonorientable Surfaces",
  "authors": [
    "Elmas Irmak"
  ],
  "comment": "13 pages, 6 figures. The paper was shortened and reorganized",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "Let $N$ be a compact, connected, nonorientable surface of genus $g$ with $n$ boundary components. Let $\\lambda$ be a simplicial map of the complex of curves, $\\mathcal{C}(N)$, on $N$ which satisfies the following: $[a]$ and $[b]$ are connected by an edge in $\\mathcal{C}(N)$ if and only if $\\lambda([a])$ and $\\lambda([b])$ are connected by an edge in $\\mathcal{C}(N)$ for every pair of vertices $[a], [b]$ in $\\mathcal{C}(N)$. We prove that $\\lambda$ is induced by a homeomorphism of $N$ if $(g, n) \\in \\{(1, 0), (1, 1), (2, 0)$, $(2, 1), (3, 0)\\}$ or $g + n \\geq 5$. Our result implies that superinjective simplicial maps and automorphisms of $\\mathcal{C}(N)$ are induced by homeomorphisms of $N$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-04T20:52:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Mxx",
      "20F38"
    ],
    "keywords": [
      "nonorientable surface",
      "boundary components",
      "homeomorphism",
      "result implies",
      "superinjective simplicial maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.1617I"
    }
  }
}