Thurston's Spinning Construction and Solutions to the Hyperbolic Gluing Equations for Closed Hyperbolic 3-Manifolds
Geometric Topology
2010-04-20 v1
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.
Keywords
Cite
@article{arxiv.1004.2992,
title = {Thurston's Spinning Construction and Solutions to the Hyperbolic Gluing Equations for Closed Hyperbolic 3-Manifolds},
author = {Feng Luo and Stephan Tillmann and Tian Yang},
journal= {arXiv preprint arXiv:1004.2992},
year = {2010}
}
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17 pages