Absolute profinite rigidity and hyperbolic geometry

• 成果类型: Article
• 署名作者: Bridson, M. R.; McReynolds, D. B.; Reid, A. W.; Spitler, R.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2020.192.3.1
• 发表日期: 2020
• 页码: 679-719
• 关键词: 3-manifolds

摘要

We construct arithmetic Kleinian groups that are profinitely rigid in the absolute sense: each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. The Bianchi group PSL(2, Z[omega]) with omega(2) + omega + 1 = 0 is rigid in this sense. Other examples include the non-uniform lattice of minimal co-volume in PSL(2, C) and the fundamental group of the Weeks manifold (the closed hyperbolic 3-manifold of minimal volume).