The Moduli Space of Hyperbolic Cone Structures

Qing Zhou

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The Moduli Space of Hyperbolic Cone Structures

Qing Zhou

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Abstract

Let $Σ$ 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 $(X, Σ)$ with all cone angle less than $2π/3$ 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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Qing Zhou. 1998-05-28. The Moduli Space of Hyperbolic Cone Structures. https://arxiv.org/abs/math/9805129

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