Thurston's Spinning Construction and Solutions to the Hyperbolic Gluing Equations for Closed Hyperbolic 3-Manifolds

Feng Luo; Stephan Tillmann; Tian Yang

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arXiv · 1004.2992

Thurston's Spinning Construction and Solutions to the Hyperbolic Gluing Equations for Closed Hyperbolic 3-Manifolds

Feng Luo·Stephan Tillmann·Tian Yang

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Abstract

We show that the hyperbolic structure on a closed, orientable, hyperbolic 3-manifold can be constructed from a solution to the hyperbolic gluing equations using any triangulation with essential edges. The key ingredients in the proof are Thurston's spinning construction and a volume rigidity result attributed by Dunfield to Thurston, Gromov and Goldman. As an application, we show that this gives a new algorithm to detect hyperbolic structures on closed 3-manifolds.

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BibTeX RIS

Feng Luo, Stephan Tillmann, Tian Yang. 2010-04-18. Thurston's Spinning Construction and Solutions to the Hyperbolic Gluing Equations for Closed Hyperbolic 3-Manifolds. https://arxiv.org/abs/1004.2992

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