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Riemann Surfaces Over Regular Maps

Published online by Cambridge University Press:  20 November 2018

Stephen E. Wilson
Stephen E. Wilson*
Affiliation:
Michigan State University East Lansing, Michigan
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The idea of one surface covering another is a useful one in the study of regular maps. Coxeter and Moser discuss a particular instance [3, p. 115] and the maps produced by Sherk [6] and Garbe [4] are formed by such coverings, though neither paper mentions that fact. In [5], Sherk explicitly constructs coverings of regular maps on the sphere.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 4 , 01 August 1978 , pp. 763 - 782
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Brahana, H. R., Regular maps and their groups, Amer. J. Math. 49 (1927), 268–284.Google Scholar
2. Coxeter, H. S. M., Regular complex polytopes (Cambridge University Press, London, 1974).Google Scholar
3. Coxeter, H. S. M. and Moser, W. O. J., Generators and relations for discrete groups (Springer- Verlag, Berlin-New York, 1972).Google Scholar
4. Garbe, D., A generalization of the regular maps of type (4,4)6,c and ﹛3,6﹜fo,c, Can. Math. Bull. 12 (1969), 293–298.Google Scholar
5. Sherk, F. A., The regular maps on a surface of genus three, Can. J. Math. 11 (1959), 452–480.Google Scholar
6. Sherk, F. A., A family of regular maps of type ﹛6,6﹜, Can. Math. Bull. (1962), 13–20.Google Scholar
7. Wilson, S. E., New techniques for the construction of regular maps, Doctoral Dissertation, Univ. of Washington, Seattle, 1976.Google Scholar