Absolute profinite rigidity and hyperbolic geometry

被引：28
|
作者：
Bridson, M. R. [1 ]
McReynolds, D. B. [2 ]
Reid, A. W. [3 ]
Spitler, R. [4 ]
机构：
[1] Univ Oxford, Math Inst, Oxford, England
[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA
[3] Rice Univ, Dept Math, Houston, TX 77251 USA
[4] McMaster Univ Hamilton, Dept Math, Hamilton, ON, Canada
来源：
ANNALS OF MATHEMATICS | 2020年 / 192卷 / 03期
基金：
美国国家科学基金会;
关键词：
Profinite completion; rigidity; hyperbolic; 3-orbifold; 3-manifold; Bianchi group; Weeks manifold; 3-MANIFOLDS;
D O I：
10.4007/annals.2020.192.3.1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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).
引用
收藏
页码：679 / 719
页数：41
相关论文
共 50 条
12345