Classes of separable two-generator free subgroups of 3-manifold groups
type: Item
instance of: scholarly article
title: Classes of separable two-generator free subgroups of 3-manifold groups
zbMATH Open document ID: 1025.57006
DOI: 10.1016/S0166-8641(02)00353-X
author: Emily Hamilton
published in: Topology and its Applications
publication date: 2003-07-29T00:00:00Z
review text: A subgroup \(H\) of a group \(G\) is called separable if for any element \(g\) in \(G\) lying outside \(H\), there exists a subgroup of \(G\) of finite index containing \(H\) and avoiding \(g\). The author shows that certain subgroups of free products with amalgamation are separable. In particular, suppose \(M_1\), \(M_2\) are compact orientable 3-manifolds, each with at least one torus on its boundary. Denote by \(T_1\), \(T_2\) these tori. Suppose the interiors of the \(M_i\) admit complete hyperbolic structures of finite volume. Let \(M\) denote the 3-manifold obtained by identifying \(T_1\) and \(T_2\) by a homeomorphism. If \(\alpha \in \pi_1(M_1)\) and \(\beta \in \pi_1(M_2)\) are loxodromic, then the subgroup of \(\pi_1(M)\) generated by \(\alpha\) and \(\beta\) is a separable subgroup of \(\pi_1(M)\).
Mathematics Subject Classification ID: 57M07
Mathematics Subject Classification ID: 20E26
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 20E06
zbMATH DE Number: 1955996
zbMATH Keywords: subgroup separability
zbMATH Keywords: free product with amalgamation
zbMATH Keywords: hyperbolic 3-manifold
reviewed by: Lee P. Neuwirth
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1955996