Thurstons spinning construction and solutions to the hyperbolic gluing equations for closed hyperbolic 3manifolds

Feng Luo Stephan Tillmann Tian Yang

Geometric Analysis and Geometric Topology mathscidoc:1912.43785

Proceedings of the American Mathematical Society, 141, (1), 335-350, 2013
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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@inproceedings{feng2013thurstons,
  title={Thurstons spinning construction and solutions to the hyperbolic gluing equations for closed hyperbolic 3manifolds},
  author={Feng Luo, Stephan Tillmann, and Tian Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205813142400349},
  booktitle={Proceedings of the American Mathematical Society},
  volume={141},
  number={1},
  pages={335-350},
  year={2013},
}
Feng Luo, Stephan Tillmann, and Tian Yang. Thurstons spinning construction and solutions to the hyperbolic gluing equations for closed hyperbolic 3manifolds. 2013. Vol. 141. In Proceedings of the American Mathematical Society. pp.335-350. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205813142400349.
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