#### Volume 16, issue 3 (2012)

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Deformation spaces of Kleinian surface groups are not locally connected

### Aaron D Magid

Geometry & Topology 16 (2012) 1247–1320
##### Abstract

For any closed surface $S$ of genus $g\ge 2$, we show that the deformation space $AH\left(S×I\right)$ of marked hyperbolic $3$–manifolds homotopy equivalent to $S$ 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.

##### Keywords
hyperbolic, Kleinian group, deformation, hyperbolic Dehn filling, drilling, locally connected
Primary: 57M50
Secondary: 30F40