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Generic Dirichlet polygons and the modular group

Published online by Cambridge University Press:  18 May 2009

A. M. Macbeath
A. M. Macbeath
Affiliation:
Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh PA. 15260
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The concept of “marked polygon”, made explicit in this paper, is implicit in all studies of the relationships between the edges and vertices of a fundamental polygon for Fuchsian group, as well as in the topology of surfaces. Once the matching of the edges under the action of the group is known, one can deduce purely combinatorially the distribution of the vertices into equivalence classes, or cycles. Knowing a little more, the order of the rotation group fixing a vertex in each cycle, we can write down a presentation for the group.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 27 , October 1985 , pp. 129 - 141
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

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