A characterization on separable subgroups of 3‐manifold groups. Issue 1 (11th November 2019)

• Record Type: Journal Article
• Authors: Sun, Hongbin
• Is Part Of: Journal of topology. Volume 13:Issue 1(2020)
• Page Start: 187
• Page End: 236
• Publication Date: 2019-11-11
• Subjects: 57M05 (primary) -- 57M50 -- 57N10 -- 20E26 (secondary); Topology -- Periodicals; 514.05
• DOI: 10.1112/topo.12128
• Languages: English
• ISSNs: 1753-8416

Abstract

Abstract: In this paper, we give a complete characterization on which finitely generated subgroups of finitely generated 3‐manifold groups are separable. Our characterization generalizes Liu's spirality character on surface subgroups of closed 3‐manifold groups. A consequence of our characterization is that, for any compact, orientable, irreducible and ∂ ‐irreducible 3‐manifold M with nontrivial torus decomposition, π 1 ( M ) is locally extended residually finite if and only if for any two adjacent pieces in the torus decomposition of M, at least one of them has a boundary component with genus at least 2.