Volume 17, issue 1 (2013)

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

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

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
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
The deformation theory of hyperbolic cone–$3$–manifolds with cone-angles less than $2\pi$

Hartmut Weiß

Geometry & Topology 17 (2013) 329–367
Abstract

We develop the deformation theory of hyperbolic cone–3–manifolds with cone-angles less than 2π, that is, contained in the interval (0,2π). In the present paper we focus on deformations keeping the topological type of the cone-manifold fixed. We prove local rigidity for such structures. This gives a positive answer to a question of A Casson.

Keywords
cone-manifolds, geometric structures on low-dimensional manifolds, hyperbolic geometry
Mathematical Subject Classification 2010
Primary: 53C25
Secondary: 57M50
References
Publication
Received: 12 April 2012
Accepted: 9 September 2012
Published: 11 March 2013
Proposed: Jean-Pierre Otal
Seconded: Simon Donaldson, Walter Neumann
Authors
Hartmut Weiß
LMU München
Mathematisches Institut
Theresienstr. 39
D-80333 München
Germany
http://www.mathematik.uni-muenchen.de/~weiss/