A two-dimensional slice through the parameter space of two-generator Kleinian groups

Elena Klimenko; Natalia Kopteva

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A two-dimensional slice through the parameter space of two-generator Kleinian groups

Elena Klimenko·Natalia Kopteva

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Abstract

We describe all real points of the parameter space of two-generator Kleinian groups with a parabolic generator, that is, we describe a certain two-dimensional slice through this space. In order to do this we gather together known discreteness criteria for two-generator groups and present them in the form of conditions on parameters. We complete the description by giving discreteness criteria for groups generated by a parabolic and a $π$-loxodromic elements whose commutator has real trace and present all orbifolds uniformized by such groups.

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Elena Klimenko, Natalia Kopteva. 2005-12-19. A two-dimensional slice through the parameter space of two-generator Kleinian groups. https://arxiv.org/abs/math/0512441

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