Automorphisms of curve complexes on nonorientable surfaces

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Atalan F., KORKMAZ M.

GROUPS GEOMETRY AND DYNAMICS, vol.8, no.1, pp.39-68, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 1
  • Publication Date: 2014
  • Doi Number: 10.4171/ggd/216
  • Journal Name: GROUPS GEOMETRY AND DYNAMICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.39-68
  • Keywords: Mapping class group, complex of curves, nonorientable surface, MAPPING CLASS-GROUPS, SUPERINJECTIVE SIMPLICIAL MAPS, INJECTIVE HOMOMORPHISMS, SUBGROUPS
  • Middle East Technical University Affiliated: Yes

Abstract

For a compact connected nonorientable surface N of genus g with n boundary components, we prove that the natural map from the mapping class group of N to the automorphism group of the curve complex of N is an isomorphism provided that g + n >= 5. We also prove that two curve complexes are isomorphic if and only if the underlying surfaces are diffeomorphic.