### Impacto

Gamboa Mutuberria, José Manuel and Bujalance, E. and Costa, A.F.
(2001)
*The Hyperelliptic Mapping Class Group Of Klein Surfaces.*
Proceedings Of The Edinburgh Mathematical Society, 44
(2).
pp. 351-363.
ISSN 0013-0915

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Official URL: http://journals.cambridge.org/abstract_S0013091599000322

## 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.

Item Type: | Article |
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Uncontrolled Keywords: | Mapping Class Group; Klein Surfaces |

Subjects: | Sciences > Mathematics > Algebra |

ID Code: | 15279 |

References: | N. L. Alling and N. Greenleaf, Foundations of the theory of Klein surfaces, Lecture Notes in Mathematics, vol. 219 (Springer, Berlin, 1971). J. S. Birman, Braids, links and mapping class groups, Annals of Mathematical Studies, vol. 82 (Princeton University Press, Princeton, NJ, 1975). J. S. Birman and D. R. Chillingworth, On the homeotopy group of a nonorientable surface, Proc. Camb. Phil. Soc. 71 (1972), 437{448. J. S. Birman and M. Hilden, On the mapping class groups of closed surfaces as covering spaces, Ann. Math. Stud. 66 (1971), 81{115. E. Bujalance, J. J. Etayo, J. M. Gamboa and G. Gromadzki, Automorphism groups of compact bordered Klein surfaces, Lecture Notes in Mathematics, vol. 1439 (Springer, Berlin, 1990). W. J. Harvey, On branch loci in Teichm¨uller space, Trans. Am. Math. Soc. 153 (1971), 387{399. W. J. Harvey and C. Maclachlan, On mapping class groups and Teichm¨uller spaces, Proc. Lond. Math. Soc. (3) 30 (1975), 496{512. A. Hatcher and W. Thurston, A presentation for the mapping class group of a closed orientable surface, Topology 19 (1980), 221{237. A. M. Macbeath, The classication of non-Euclidean plane crystallographic groups, Can. J. Math. 19 (1967), 1192{1205. A. M. Macbeath and D. Singerman, Spaces of subgroups and Teichm¨uller space, Proc. Lond. Math. Soc. 31 (1975), 211{256. W. Magnus, Braids and Riemann surfaces, Commun. Pure Appl. Math. 25 (1972), 151{161. W. Thurston, Three-dimensional geometry and topology, vol. 1 (Princeton University Press, Princeton, NJ, 1997). H. Zieschang, On the homeotopy groups of surfaces, Math. Annln 206 (1973), 1{21. |

Deposited On: | 21 May 2012 10:36 |

Last Modified: | 06 Feb 2014 10:20 |

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