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

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

2009-04-29

arxiv.org/abs/0904.4568v2

Mathematics

Differential Geometry

Minor corrections; references updated

Scientific paper

We develop the deformation theory of hyperbolic cone-3-manifolds with
cone-angles less than $2\pi$, i.e. contained in the interval $(0,2\pi)$. 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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