Parabolics on the Boundary of the Deformation Space of a Kleinian Group

Abstract

We present a condition on a loxodromic element L of a Kleinian group G which guarantees that L cannot be made parabolic on the boundary of the deformation space of G, namely, that the fixed points of L are separated by the limit set of a subgroup F of G which is a finitely generated quasifuchsian group of the first kind. The proof uses the collar theorem for short geodesics in hyperbolic 3-manifolds.