Discreteness of the complex hyperbolic ultra-parallel triangle groups

Wei Liao; Baohua Xie

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arXiv · 2504.04407

Discreteness of the complex hyperbolic ultra-parallel triangle groups

Wei Liao·Baohua Xie

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Abstract

We prove that a family of complex hyperbolic ultra-parallel $[m_1, m_2, m_3]$-triangle group representations, where $ m_3 > 0 $, is discrete and faithful if and only if the isometry $ R_1(R_2R_1)^nR_3 $ is non-elliptic for some positive integer $ n $. Additionally, we investigate the special case where $ m_3 = 0 $ and provide a substantial improvement upon the main result by Monaghan, Parker, and Pratoussevitch.

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BibTeX RIS

Wei Liao, Baohua Xie. 2025-04-06. Discreteness of the complex hyperbolic ultra-parallel triangle groups. https://arxiv.org/abs/2504.04407

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