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

• 成果类型: Article
• 署名作者: Liu, Yi
• 署名单位: Peking University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01155-4
• 发表日期: 2023
• 页码: 741-804
• 关键词: twisted alexander polynomials; profinite rigidity; graph manifolds; conjugacy separability; completions; NORM

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.