We give a construction for new families of thin subgroups inside SL(4,R). In particular, we show that the fundamental group of a closed hyperbolic 3-manifold can be isomorphic to a thin subgroup of a lattice. © The Author(s) 2013.

We show that for certain arithmetic groups, geometrically finite subgroups are the intersection of finite index subgroups containing them. Examples are the Bianchi groups and the Seifert-Weber dodecahedral space. In particular, for manifolds commensurable with these groups, immersed incompressible surfaces lift to embeddings in a finite sheeted covering.