Geometry & Topology

Deformation spaces of Kleinian surface groups are not locally connected

Aaron D Magid

Full-text: Open access

Abstract

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

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

Dates
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
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
Secondary: 30F40: Kleinian groups [See also 20H10]

Keywords
hyperbolic Kleinian group deformation hyperbolic Dehn filling drilling locally connected

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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