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ON THE CONNECTEDNESS OF THE BRANCH LOCI OF NON-ORIENTABLE UNBORDERED KLEIN SURFACES OF LOW GENUS

Part of: Low-dimensional topology Special aspects of infinite or finite groups Riemann surfaces Other groups of matrices

Published online by Cambridge University Press:  22 December 2014

E. BUJALANCE ,
J. J. ETAYO ,
E. MARTÍNEZ  and
B. SZEPIETOWSKI
E. BUJALANCE
Affiliation:
Departamento de Matemáticas Fundamentales, UNED, Paseo Senda del Rey 9, 28040-Madrid, Spain e-mail: ebujalance@mat.uned.es
J. J. ETAYO
Affiliation:
Departamento de Álgebra, Facultad de Matemáticas, Universidad Complutense, 28040-Madrid, Spain e-mail: jetayo@mat.ucm.es
E. MARTÍNEZ
Affiliation:
Departamento de Matemáticas Fundamentales, UNED, Paseo Senda del Rey 9, 28040-Madrid, Spain e-mail: emartinez@mat.uned.es
B. SZEPIETOWSKI
Affiliation:
Institute of Mathematics, University of Gdańsk. Ul. Wita, Stwosza 57, 80-952 Gdańsk, Poland e-mail: blaszep@mat.ug.edu.pl
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Abstract

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This paper is devoted to determine the connectedness of the branch loci of the moduli space of non-orientable unbordered Klein surfaces. We obtain a result similar to Nielsen's in order to determine topological conjugacy of automorphisms of prime order on such surfaces. Using this result we prove that the branch locus is connected for surfaces of topological genus 4 and 5.

MSC classification

Primary: 57M60: Group actions in low dimensions
Secondary: 20F05: Generators, relations, and presentations 20H10: Fuchsian groups and their generalizations 30F50: Klein surfaces
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 57 , Issue 1 , January 2015 , pp. 211 - 230
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

References

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