The deformation theory of hyperbolic cone-3-manifolds with cone-angles less than 2π
Abstract
We develop the deformation theory of hyperbolic cone-3-manifolds with cone-angles less than 2π, i.e. 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.
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