Geometric finite amalgamations of hyperbolic 3manifold groups are not LERF
Geometric finite amalgamations of hyperbolic 3manifold groups are not LERF

Hongbin Sun , Rutgers University
Fine Hall 314
A group G is called LERF if the property that an element not lying in a finitely generated subgroup is visible via a finite quotient of G. LERFness of groups is closed related with lowdimensional topology: whether an immersed \pi_1injective object can be lifted to embedding in some finite cover. We will show that, for any two finite volume hyperbolic 3manifolds, the amalgamations of their fundamental groups along nontrivial geometrically finite subgroups are always not LERF. A consequence of this result is: all arithmetic hyperbolic manifolds with dimension at least 4, with possible exceptions in 7dimensional manifolds defined by the octonion, their fundamental groups are not LERF.