#### Volume 17, issue 1 (2013)

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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 $2\pi$, that is, contained in the interval $\left(0,2\pi \right)$. 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
Primary: 53C25
Secondary: 57M50
##### Publication
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/