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