TOPOLOGICALLY CONJUGATE KLEINIAN-GROUPS

Two Kleinian groups Gamma(1) and Gamma(2) are said to be topologically conjugate when there is a homeomorphism f : S-2 --> S-2 such that f G amma(1)f(-1) = Gamma(2). It is conjectured that if two Kleinian groups Gamma(1) and Gamma(2) are topologically conjugate, one is a quasi-con formal deformation of the other. In this paper generalizing Minsky's r esult, we shall prove that this conjecture is true when Gamma(1) is fi nitely generated and freely indecomposable, and the injectivity radii of all points of H-3/Gamma(1) and H-3/Gamma(2) are bounded below by a positive constant.