Deformation spaces of Kleinian surface groups are not locally connected

Magid, Aaron D

doi:10.2140/gt.2012.16.1247

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Deformation spaces of Kleinian surface groups are not locally connected

Aaron D Magid

Geometry & Topology 16 (2012) 1247–1320

DOI: 10.2140/gt.2012.16.1247

Abstract

For any closed surface $S$ of genus $g \geq 2$ , we show that the deformation space $A H (S \times I)$ 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

Volume 16, issue 3 (2012)