## NonLERFness of groups of certain mixed 3-manifolds and arithmetic hyperbolic $n$-manifolds

Hongbin Sun

University of California, Berkeley

May 3, 2016

I will show that the groups of mixed 3-manifolds containing arithmetic hyperbolic pieces and the groups of certain noncompact arithmetic hyperbolic $n$-manifolds ($n > 3$) are not LERF. The main ingredient is a study of the set of virtual fibered boundary slopes for cusped hyperbolic 3-manifolds, and some specialty of Bianchi manifolds.