Geometry & Topology

Deformation spaces of Kleinian surface groups are not locally connected

Aaron D Magid

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For any closed surface S of genus g2, 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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 30F40: Kleinian groups [See also 20H10]

hyperbolic Kleinian group deformation hyperbolic Dehn filling drilling locally connected


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.

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