Seminars & Colloquia Calendar
A characterization of separable subgroups of 3-manifold groups
Hongbin Sun (Rutgers)
Location: Hill 525
Date & time: Tuesday, 04 December 2018 at 3:40PM - 4:40PM
Abstract: The subgroup separability is a property in group theory that is closely related to low dimensional topology, especially lifting pi_1-injective immersed objects in a space to be embedded in some finite cover and the virtual Haken conjecture of 3-manifolds resolved by Agol. 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 pi_1-injective immersed surface subgroups of closed 3-manifold groups. A consequence of our characterization is that, for any compact, orientable, irreducible and boundary-irreducible 3-manifold M with nontrivial torus decomposition, pi_1(M) is LERF 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.