Thurston’s Spinning Construction and Solutions to the Hyperbolic Gluing Equations for Closed Hyperbolic 3–manifolds
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چکیده
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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تاریخ انتشار 2012