New non-arithmetic complex hyperbolic lattices

• 成果类型: Article
• 署名作者: Deraux, Martin; Parker, John R.; Paupert, Julien
• 署名单位: Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Durham University; Arizona State University; Arizona State University-Tempe
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0600-1
• 发表日期: 2016
• 页码: 681-771
• 关键词: fake projective-planes; triangle groups; moduli space; geometry; superrigidity; monodromy; domains

摘要

We produce a family of new, non-arithmetic lattices in PU(2, 1). All previously known examples were commensurable with lattices constructed by Picard, Mostow, and Deligne-Mostow, and fell into nine commensurability classes. Our groups produce five new distinct commensurability classes. Most of the techniques are completely general, and provide efficient geometric and computational tools for constructing fundamental domains for discrete groups acting on the complex hyperbolic plane.