For i = 1, 2, let G i be cocompact groups of isometries of hyper-bolic space H n of real dimension n, n ≥ 3. Let H i ⊂ G i be infinite index quasiconvex subgroups satisfying one of the following conditions: 1) limit set of H i is a codimension one topological sphere. 2) limit set of H i is an even dimensional topological sphere. 3) H i is a codimension one… (More)