Doubles of groups and hyperbolic LERF 3-manifolds

• 成果类型: Article
• 署名作者: Gitik, R
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/121056
• 发表日期: 1999
• 页码: 775-806
• 关键词: negatively curved groups; surface groups; separability properties; SUBGROUPS; MANIFOLDS; THEOREM; graphs

摘要

We show that the quasiconvex subgroups in doubles of certain negatively curved groups are closed in the profinite topology. This allows us to construct the first known large family of hyperbolic 3-manifolds such that any finitely generated subgroup of the fundamental group of any member of the family is closed in the profinite topology.