2005/12/19 by Elena Klimenko, Klimenko, Elena, Natalia Kopteva +1
Mathematics · #20H10 #22E40 #30F40 (primary) #57M60 (secondary) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.math/0512441
openalex publication_date 2005/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.