Classes of separable two-generator free subgroups of 3-manifold groups

In this paper, we consider subgroup separability of free products with amalgamation of Kleinian groups of finite covolume. Specifically, we prove the following. Let M1 and M2 be compact orientable 3-manifolds with non-empty boundary whose interiors admit complete hyperbolic structures of finite volume. Fix boundary components T1∈∂M1 and T2∈∂M2, and let f :T1→T2 be a homeomorphism. Let M be the manifold obtained by identifying M1 and M2 along the fixed boundary components via f. If α and β are loxodromic elements of π1(M1) and π1(M2), respectively, then 〈α,β〉 is a separable subgroup of π1(M).