The Moduli Space of Hyperbolic Cone Structures

Details The Moduli Space of Hyperbolic Cone Structures The Moduli Space of Hyperbolic Cone Structures

1998-05-28

arxiv.org/abs/math/9805129v1

J. Differential Geometry, 51(1999), 517-550

Mathematics

Geometric Topology

29 pages

Scientific paper

Let $\Sigma$ be a hyperbolic link with $m$ components in a 3-dimensional manifold $X$. In this paper, we will show that the moduli space of marked hyperbolic cone structures on the pair $(X, \Sigma)$ with all cone angle less than $2\pi /3$ is an $m$-dimensional open cube, parameterized naturally by the $m$ cone angles. As a corollary, we will give a proof of a special case of Thurston's geometrization theorem for orbifolds.

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