The deformation theory of hyperbolic cone–3–manifolds with cone-angles less than 2π

Weiß, Hartmut

doi:10.2140/gt.2013.17.329

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

The deformation theory of hyperbolic cone–$3$–manifolds with cone-angles less than $2\pi$

Hartmut Weiß

Geometry & Topology 17 (2013) 329–367

DOI: 10.2140/gt.2013.17.329

Abstract

We develop the deformation theory of hyperbolic cone–3–manifolds with cone-angles less than $2 π$ , that is, contained in the interval $(0, 2 π)$ . 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/

Volume 17, issue 1 (2013)