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 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/