Finite-volume hyperbolic 3-manifolds are almost determined by their finite quotient groups

被引：4
|
作者：
Liu, Yi [1 ]
机构：
[1] Peking Univ, Beijing Int Ctr Math Res, Beijing 100871, Peoples R China
来源：
INVENTIONES MATHEMATICAE | 2023年 / 231卷 / 02期
基金：
国家重点研发计划;
关键词：
Profinite completion; Hyperbolic geometry; 3-manifolds; Fixed point theory; TWISTED ALEXANDER POLYNOMIALS; PROFINITE RIGIDITY; GRAPH MANIFOLDS; CONJUGACY SEPARABILITY; COMPLETIONS; NORM;
D O I：
10.1007/s00222-022-01155-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For any orientable finite-volume hyperbolic 3-manifold, this paper proves that the profinite isomorphism type of the fundamental group uniquely determines the isomorphism type of the first integral cohomology, as marked with the Thurston norm and the fibered classes; moreover, up to finite ambiguity, the profinite isomorphism type determines the isomorphism type of the fundamental group, among the class of finitely generated 3-manifold groups.
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页码：741 / 804
页数：64
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