## 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.## References

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## Additional Information

**Feng Luo**- Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08854
- MR Author ID: 251419
- Email: fluo@math.rutgers.edu
**Stephan Tillmann**- Affiliation: School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072, Australia
- MR Author ID: 663011
- ORCID: 0000-0001-6731-0327
- Email: tillmann@maths.uq.edu.au
**Tian Yang**- Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08854
- Email: tianyang@math.rutgers.edu
- Received by editor(s): October 2, 2010
- Received by editor(s) in revised form: April 8, 2011
- Published electronically: August 17, 2012
- Additional Notes: Research of the first and third authors was supported in part by the NSF

Research of the second author was partially funded by a UQ New Staff Research Start-Up Fund and under the Australian Research Council’s Discovery funding scheme (DP1095760) - Communicated by: Daniel Ruberman
- © Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**141**(2013), 335-350 - MSC (2010): Primary 57M25, 57N10
- DOI: https://doi.org/10.1090/S0002-9939-2012-11220-1
- MathSciNet review: 2988735