Finite rigid sets in curve complexes of nonorientable surfaces

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Ilbira S., Korkmaz M.

GEOMETRIAE DEDICATA, vol.206, pp.83-103, 2020 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 206
  • Publication Date: 2020
  • Doi Number: 10.1007/s10711-019-00478-6
  • Journal Name: GEOMETRIAE DEDICATA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.83-103
  • Keywords: Nonorientable surface, Mapping class group, Curve complex, Finite rigid set, SIMPLICIAL MAPS, AUTOMORPHISMS
  • Open Archive Collection: AVESIS Open Access Collection
  • Middle East Technical University Affiliated: Yes

Abstract

A rigid set in a curve complex of a surface is a subcomplex such that every locally injective simplicial map from the set into the curve complex is induced by a homeomorphism of the surface. In this paper, we find finite rigid sets in the curve complexes of connected nonorientable surfaces of genus g with n holes for g + n not equal 4.