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On discrete generalised triangle groups

Published online by Cambridge University Press:  20 January 2009

M. Hagelberg ,
C. MacLachlan  and
G. Rosenberger
M. Hagelberg
Affiliation:
Institut für Mathematik, Ruhr-Universität Bochum, 4630 Bochum 1, Germany
C. MacLachlan
Affiliation:
Department of Mathematical Sciences, University of Aberdeen, Aberdeen AB9 2RY, Scotland
G. Rosenberger
Affiliation:
Fachbereich Mathematik, Universität Dortmund, 4600 Dortmund 50, Germany
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Abstract

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A generalised triangle group has a presentation of the form

where R is a cyclically reduced word involving both x and y. When R = xy, these classical triangle groups have representations as discrete groups of isometrics of S2, R2, H2 depending on

In this paper, for other words R, faithful discrete representations of these groups in Isom +H3 = PSL(2, C) are considered with particular emphasis on the case R = [x, y] and also on the relationship between the Euler characteristic χ and finite covolume representations.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 3 , October 1995 , pp. 397 - 412
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

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