Mathematics Colloquium

Subgroup separability is a purely group theoretical property that topologists are interested in. It is related with lifting a \pi_1-injective immersed object to be embedded in some finite cover, and in particular the virtual Haken conjecture. In this talk, I will give many new examples of subgroup non-separable groups that come from topology. These groups include: groups of mixed 3-manifolds, amalgamation of finite volume hyperbolic 3-manifold groups along geometrically finite subgroups, and most arithmetic hyperbolic manifold groups with dimension at least 4. The proof of subgroup non-separability heavily uses consequences and tools of Agol's works on subgroup separability of hyperbolic 3-manifold groups.