Abstract
AbstractIn this paper, we study the discreteness criteria for nonelementary subgroups of U(1,n;ℂ) acting on complex hyperbolic space. Several discreteness criteria are obtained. As applications, we obtain a classification of nonelementary subgroups of U(1,n;ℂ) and show that any dense subgroup of SU(1,n;ℂ) contains a dense subgroup generated by at most n elements when n≥2. We also obtain a necessary and sufficient condition for the normalizer of a discrete and nonelementary subgroup in SU(1,n;ℂ) to be discrete.
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