Geometry & Topology 16 (2012) 1247–1320

DOI: 10.2140/gt.2012.16.1247

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

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