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THE HYPERELLIPTIC MAPPING CLASS GROUP OF KLEIN SURFACES

Published online by Cambridge University Press:  20 January 2009

E. Bujalance ,
A. F. Costa  and
J. M. Gamboa
E. Bujalance
Affiliation:
Departamento de Matemáticas Fundamentales, Facultad de Ciencias, Universidad Nacional de Educación a Distancia, Senda del Rey, 28040 Madrid, Spain
A. F. Costa
Affiliation:
Departamento de Matemáticas Fundamentales, Facultad de Ciencias, Universidad Nacional de Educación a Distancia, Senda del Rey, 28040 Madrid, Spain
J. M. Gamboa
Affiliation:
Departamento de Algebra, Facultad de Ciencias Matemáticas, Universidad Complutense, 28040 Madrid, Spain
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Abstract

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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

Keywords

Klein surfacehyperelliptic Klein surfacemapping class groupreal algebraic curvemoduli space
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 2 , June 2001 , pp. 351 - 363
Copyright
Copyright © Edinburgh Mathematical Society 2001