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The deformation theory of hyperbolic cone-3-manifolds with cone-angles less than \(2\pi\). (English) Zbl 1262.53032
Summary: We develop the deformation theory of hyperbolic cone-3-manifolds with cone-angles less than \(2\pi \), that is, 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.

MSC:
53C20 Global Riemannian geometry, including pinching
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