Thurston’s spinning construction and solutions to the hyperbolic gluing equations for closed hyperbolic 3–manifolds

Luo, Feng; Tillmann, Stephan; Yang, Tian

doi:10.1090/S0002-9939-2012-11220-1

Thurston’s spinning construction and solutions to the hyperbolic gluing equations for closed hyperbolic 3–manifolds
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by Feng Luo, Stephan Tillmann and Tian Yang PDF

Proc. Amer. Math. Soc. 141 (2013), 335-350 Request permission

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 and small Seifert fibred structures on closed 3–manifolds.

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