Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-28T09:26:01.061Z Has data issue: false hasContentIssue false
  • English
  • Français

DOUBLES OF KLEIN SURFACES

Published online by Cambridge University Press:  30 March 2012

ANTONIO F. COSTA ,
WENDY HALL  and
DAVID SINGERMAN
ANTONIO F. COSTA
Affiliation:
Departamento de Matemáticas Fundamentales, UNED, Madrid 28040, Spain
WENDY HALL
Affiliation:
Department of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, United Kingdom
DAVID SINGERMAN
Affiliation:
Department of Mathematics, University of Southampton, Southampton SO17 1BJ, United Kingdom
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Historical note. A non-orientable surface of genus 2 (meaning 2 cross-caps) is popularly known as the Klein bottle. However, the term Klein surface comes from Felix Klein's book “On Riemann's Theory of Algebraic Functions and their Integrals” (1882) where he introduced such surfaces in the final chapter.

Keywords

30F5030F10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 3 , September 2012 , pp. 507 - 515
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

REFERENCES

1.Alling, N. L. and Greenleaf, N., Foundations of the theory of Klein surfaces. Lecture Notes in Mathematics, vol. 219 (Springer-Verlag, Berlin-New York, 1971), ix+117 pp.CrossRefGoogle Scholar
2.Bujalance, E., Costa, A. F., Natanzon, S. M. and Singerman, D., Involutions of compact Klein surfaces, Math. Z. 211 (3) (1992), 461–478.CrossRefGoogle Scholar
3.Bujalance, E., Etayo, J. J., Gamboa, J. M. and Gromadzki, G., Automorphism groups of compact bordered Klein surfaces. A combinatorial approach. Lecture Notes in Mathematics, vol. 1439 (Springer-Verlag, Berlin, 1990), xiv+201 pp.CrossRefGoogle Scholar
4.Hall, W., Automorphisms and coverings of Klein surfaces, PhD Thesis (University of Southampton, 1977).Google Scholar
5.Hoare, A. H. M. and Singerman, D., The orientability of subgroups of plane groups. Groups–-St. Andrews 1981 (St. Andrews, 1981), pp. 221–227, London Math. Soc. Lecture Note Ser., vol. 71, (Cambridge University Press, Cambridge, 1982).Google Scholar
6.Singerman, D., On the structure of non-euclidean crystallographic groups, Proc. Camb. Phil. Soc. 76 (1974), 233–240.CrossRefGoogle Scholar