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

Abstract

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.

Minor corrections; references updated

References in corpus (2)

• Deforming Euclidean cone 3-manifolds
• Complex twist flows on surface group representations and the local shape of the deformation space of hyperbolic cone-3-manifolds

Cited by in corpus (3)

• Combinatorial Ricci flows and the hyperbolization of a class of compact 3-manifolds
• Complex twist flows on surface group representations and the local shape of the deformation space of hyperbolic cone-3-manifolds
• Degeneration of 3-dimensional hyperbolic cone structures with decreasing cone angles