Rigidity and topological conjugates of topologically tame Kleinian groups

Minsky proved that two Kleinian groups $G_1$ and $G_2$ are quasi-conformally conjugate if they are freely indecomposable, the injectivity radii at all points of $\bold{H}^3/G_1$, $\bold{H}^3/G_2$ are bounded below by a positive constant, and there is a homeomorphism $h$ from a topological core of $\bold{H}^3/G_1$ to that of $\bold{H}^3/G_2$ such that $h$ and $h^{-1}$ map ending laminations to ending laminations. We generalize this theorem to the case when $G_1$ and $G_2$ are topologically tame but may be freely decomposable under the same assumption on the injectivity radii. As an application, we prove that if a Kleinian group is topologically conjugate to another Kleinian group which is topologically tame and not a free group, and both Kleinian groups satisfy the assumption on the injectivity radii as above, then they are quasi-conformally conjugate.