| For any closed surface S of genus g ≥ 2, we show that the deformation space of marked hyperbolic 3-manifolds homotopy equivalent to S, AH(S x I), is not locally connected. This proves a conjecture of Bromberg who recently proved that the space of Kleinian punctured torus groups is not locally connected. Playing an essential role in our proof is a new version of the filling theorem that is based on the theory of cone-manifold deformations developed by Hodgson, Kerckhoff, and Bromberg. |
