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DISCRETE AND DENSE SUBGROUPS ACTING ON COMPLEX HYPERBOLIC SPACE

Part of: Riemann surfaces

Published online by Cambridge University Press:  01 October 2008

WENSHENG CAO
WENSHENG CAO*
Affiliation:
Department of Mathematics and Physics, Wuyi University, Jiangmen 529020, China (email: [email protected])
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Abstract

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In 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.

Keywords

discreteness criterionnonelementary subgroupdense subgroupnormalizer

MSC classification

Secondary: 30F40: Kleinian groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 2 , October 2008 , pp. 211 - 224
Copyright
Copyright © 2008 Australian Mathematical Society

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