A discreteness condition for subgroups of \(\mathbf{PU}(2, 1)\)

DOI10.1007/s40315-019-00275-yzbMath1480.20118OpenAlexW2945388942MaRDI QIDQ2326832

Bao-Hua Xie, Xue-Jing Ren, Yue Ping Jiang

Publication date: 10 October 2019

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40315-019-00275-y

zbMATH Keywords

bisectorcomplex hyperbolic spacediscreteness condition

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Discrete subgroups of Lie groups (22E40) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10)

Cites Work

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• On a remarkable class of polyhedra in complex hyperbolic space
• The moduli space of the modular group in complex hyperbolic geometry
• Decomposition of complex hyperbolic isometries by two complex symmetries
• Real reflections, commutators, and cross-ratios in complex hyperbolic space
• Doubly generated Fuchsian groups
• An algorithm for 2-generator Fuchsian groups
• Traces, Cross-Ratios and 2-Generator Subgroups of SU(2, 1)
• A Poincaré's polyhedron theorem for complex hyperbolic geometry

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