Volume 16, issue 3 (2012)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 22
Issue 6, 3145–3760
Issue 5, 2511–3144
Issue 4, 1893–2510
Issue 3, 1267–1891
Issue 2, 645–1266
Issue 1, 1–644

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Other MSP Journals
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