Mapping class groups of nonorientable surfaces


Korkmaz M.

GEOMETRIAE DEDICATA, vol.89, no.1, pp.109-133, 2002 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 89 Issue: 1
  • Publication Date: 2002
  • Title of Journal : GEOMETRIAE DEDICATA
  • Page Numbers: pp.109-133
  • Keywords: mapping class groups, nonorientable surfaces, real-analytic diffeomorphism of the circle, HOMOLOGY

Abstract

We obtain a finite set of generators for the mapping class group of a nonorientable surface with punctures. We then compute the first homology group of the mapping class group and certain subgroups of it. As an application we prove that the image of a homomorphism from the mapping class group of a nonorientable surface of genus at least nine to the group of real-analytic diffeomorphisms of the circle is either trivial or of order two.