Naomi Andrew

Free-by-cyclic groups and subgroup (non)-separability

A group is said to be subgroup separable (sometimes "LERF") if for any finitely generated subgroup, and any element in its complement, there is a finite quotient witnessing this. This property holds for free and surface groups, as well as for the fundamental groups of geometric three manifolds. But it fails for (for instance) the fundamental groups of graph manifolds.

I will discuss this property, and strategies to prove or disprove that it holds for your favourite group, with a focus on what is known for free-by-cyclic groups. This is ongoing work, joint with Bering, Kudlinska, Qing and Vidussi.