Ideal triangle groups, dented tori, and numerical analysis

• 成果类型: Article
• 署名作者: Schwartz, RE
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/2661362
• 发表日期: 2001
• 页码: 533-598
• 关键词: complex hyperbolic space; REPRESENTATIONS; geometry

摘要

We prove the Goldman-Parker Conjecture: A complex hyperbolic ideal triangle group is discretely embedded in PU(2, 1) if and only if the product of its three standard generators is not elliptic. We also prove that such a group is indiscrete if the product of its three standard generators is elliptic. A novel feature of this paper is that it uses a rigorous computer assisted proof to deal with difficult geometric estimates.