Geometry & Topology
- Geom. Topol.
- Volume 16, Number 3 (2012), 1247-1320.
Deformation spaces of Kleinian surface groups are not locally connected
For any closed surface of genus , we show that the deformation space of marked hyperbolic –manifolds homotopy equivalent to 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.
Geom. Topol., Volume 16, Number 3 (2012), 1247-1320.
Received: 23 March 2010
Revised: 19 January 2012
Accepted: 20 March 2012
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 30F40: Kleinian groups [See also 20H10]
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