Deformation Spaces of Kleinian Surface Groups are not Locally Connected.

[摘要] For any closed surface S of genus g at least 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.

[发布机构] University of Michigan

[效力级别] Mathematics

[关键词] Deformation Spaces of Hyperbolic 3-manifolds;Mathematics;Science;Mathematics