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Convex fundamental regions for Fuchsian groups

Published online by Cambridge University Press:  24 October 2008

P. Nicholls  and
R. Zarrow
P. Nicholls
Affiliation:
Northern Illinois University, De Kalb
R. Zarrow
Affiliation:
Northern Illinois University, De Kalb
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Extract

1. Introduction. Let G be a Fuchsian group which acts on the unit disc Δ. A fundamental region D for G acting in Δ is a subset of Δ such that D is open and connected and each point of Δ is G-equivalent to exactly one point in D or at least one point in D̅ (the closure of D in Δ). Throughout this paper we consider only fundamental regions which are (hyperbolically) convex. Beardon has shown (2) that it is possible for a convex fundamental region to have certain undesirable properties. It can happen that a convex region is not locally finite, i.e. there exist points of Δ where infinitely many G images of D accumulate. For a domain D we denote by F the set of such points.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 84 , Issue 3 , November 1978 , pp. 507 - 518
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

REFERENCES

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