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

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

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.