Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

THE HYPERELLIPTIC MAPPING CLASS GROUP OF KLEIN SURFACES

E. Bujalancea1, A. F. Costaa1 and J. M. Gamboaa2

a1 Departamento de Matemáticas Fundamentales, Facultad de Ciencias, Universidad Nacional de Educación a Distancia, Senda del Rey, 28040 Madrid, Spain

a2 Departamento de Algebra, Facultad de Ciencias Matemáticas, Universidad Complutense, 28040 Madrid, Spain

Abstract

In this paper we study the algebraic structure of the hyperelliptic mapping class group of Klein surfaces, which is closely related to the mapping class group of punctured discs. This group plays an important role in the study of the moduli space of hyperelliptic real algebraic curves. Our main result provides a presentation by generators and relations for the hyperelliptic mapping class group of surfaces of prescribed topological type.

AMS 2000 Mathematics subject classification: Primary 14H10; 20H10; 30F50

(Received March 24 1999)

Keywords

  • Klein surface;
  • hyperelliptic Klein surface;
  • mapping class group;
  • real algebraic curve;
  • moduli space