{
  "id": "1907.09042",
  "version": "v1",
  "published": "2019-07-21T22:03:35.000Z",
  "updated": "2019-07-21T22:03:35.000Z",
  "title": "A note on the curve complex of the 3-holed projective plane",
  "authors": [
    "Błażej Szepietowski"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $S$ be a projective plane with $3$ holes. We prove that there is an exhaustion of the curve complex $\\mathcal{C}(S)$ by a sequence of finite rigid sets. As a corollary, we obtain that the group of simplicial automorphisms of $\\mathcal{C}(S)$ is isomorphic to the mapping class group $\\mathrm{Mod}(S)$. We also prove that $\\mathcal{C}(S)$ is quasi-isometric to a simplicial tree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-21T22:03:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "curve complex",
      "projective plane",
      "finite rigid sets",
      "mapping class group",
      "simplicial automorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}