Discreteness of the complex hyperbolic ultra-parallel triangle groups
Abstract
We prove that a family of complex hyperbolic ultra-parallel [m1, m2, m3]-triangle group representations, where \( m3 > 0 \), is discrete and faithful if and only if the isometry \( R1(R2R1)nR3 \) is non-elliptic for some positive integer \( n \). Additionally, we investigate the special case where \( m3 = 0 \) and provide a substantial improvement upon the main result by Monaghan, Parker, and Pratoussevitch.
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