Abstract
This paper is concerned with torsion-free Kleinian groups that are generated by two parabolic transformations. Our main result is that every such group of the second kind is geometrically finite; this is in response to a question raised by Riley. We also show that in the natural one (complex) dimensional setting, the space of torsion-free Kleinian groups of the second kind is path-connected.
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The first author was supported in part by NSF Grant #8701774.
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Maskit, B., Swarup, G. Two parabolic generator kleinian groups. Israel J. Math. 64, 257–266 (1988). https://doi.org/10.1007/BF02882422
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DOI: https://doi.org/10.1007/BF02882422