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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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 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.

Keywords
hyperbolic, Kleinian group, deformation, hyperbolic Dehn filling, drilling, locally connected
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 30F40
References
Publication
Received: 23 March 2010
Revised: 19 January 2012
Accepted: 20 March 2012
Published: 10 July 2012
Proposed: Danny Calegari
Seconded: David Gabai, Walter Neumann
Authors
Aaron D Magid
Department of Mathematics
University of Maryland
1301 Campus Drive
College Park MD 20742
USA