## Geometry & Topology

### Deformation spaces of Kleinian surface groups are not locally connected

Aaron D Magid

#### Abstract

For any closed surface $S$ of genus $g≥2$, we show that the deformation space $AH(S×I)$ 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.

#### Article information

Source
Geom. Topol., Volume 16, Number 3 (2012), 1247-1320.

Dates
Revised: 19 January 2012
Accepted: 20 March 2012
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732437

Digital Object Identifier
doi:10.2140/gt.2012.16.1247

Mathematical Reviews number (MathSciNet)
MR2967052

Zentralblatt MATH identifier
1257.57023

Subjects
Primary: 57M50: Geometric structures on low-dimensional manifolds

#### Citation

Magid, Aaron D. Deformation spaces of Kleinian surface groups are not locally connected. Geom. Topol. 16 (2012), no. 3, 1247--1320. doi:10.2140/gt.2012.16.1247. https://projecteuclid.org/euclid.gt/1513732437

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