Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-26T08:07:48.707Z Has data issue: false hasContentIssue false
  • English
  • Français

A family of conformally asymmetric Riemann surfaces

Published online by Cambridge University Press:  18 May 2009

Brent Everitt
Brent Everitt
Affiliation:
Department of Mathematical Sciences, University of Aberdeen, Aberdeen AB9 2TY, United Kingdom
Rights & Permissions [Opens in a new window]

Abstract

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.

We give explicit examples of asymmetric Riemann surfaces (that is, Riemann surfaces with trivial conformal automorphism group) for all genera g ≥ 3. The technique uses Schreier coset diagrams to construct torsion-free subgroups in groups of signature (0; 2,3,r) for certain values of r.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 39 , Issue 2 , May 1997 , pp. 221 - 225
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

REFERENCES

1.Borel, A., Commensurability classes and volumes of hyperbolic 3-manifolds, Ann. Sc. Norm. Sup. Pisa, 8 (1981), 1–33.Google Scholar
2.Mednyh, A. D., On an example of a compact Riemann surface with trivial automorphism group, Dokl. Akad. Nauk. SSSR, 237(1) (1977), 1396–1398.Google Scholar
3.Singerman, D., Subgroups of Fuchsian groups and finite permutation groups. Bull. London Math. Soc., 2 (1970), 319–323.CrossRefGoogle Scholar
4.Singerman, D., Automorphisms of maps, permutation groups and Riemann surfaces. Bull. London Math. Soc. 8 (1976), 65–68.CrossRefGoogle Scholar
5.Takeuchi, K., Arithmetic triangle groups, J. Math. Soc. Japan, 29 (1977), 91–106.Google Scholar
6.Zassenhaus, H., The theory of groups (Chelsea Publishing Company, 1949).Google Scholar