Journal of Lie Theory, Vol. 11, No. 2, pp. 491-503 (2001)

Some Examples of Discrete Groups and Hyperbolic Orbifolds of Infinite Volume

Elena Klimenko

Department of Mathematics
Technion-Israel Institute of Technology
Haifa 32000

Abstract: We study the class of two-generator subgroups of $ PSL(2, C)$ with real parameters which was introduced recently by Gehring, Gilman, and Martin. We give criteria for discreteness of non-elementary and non-Fuchsian groups of this class that are generated by two hyperbolic elements. We construct all hyperbolic orbifolds uniformized by the discrete groups of such type. The orbifolds described are of infinite volume.

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