Thurston's spinning construction and solutions to the hyperbolic gluing equations for closed hyperbolic 3-manifolds

Luo, Feng, Tillmann, Stephan and Yang, Tian (2012) Thurston's spinning construction and solutions to the hyperbolic gluing equations for closed hyperbolic 3-manifolds. Proceedings of the American Mathematical Society, 141 1: 335-350. doi:10.1090/S0002-9939-2012-11220-1


Author Luo, Feng
Tillmann, Stephan
Yang, Tian
Title Thurston's spinning construction and solutions to the hyperbolic gluing equations for closed hyperbolic 3-manifolds
Journal name Proceedings of the American Mathematical Society   Check publisher's open access policy
ISSN 0002-9939
1088-6826
Publication date 2012-01-01
Sub-type Article (original research)
DOI 10.1090/S0002-9939-2012-11220-1
Open Access Status DOI
Volume 141
Issue 1
Start page 335
End page 350
Total pages 16
Place of publication Providence, RI, United States
Publisher American Mathematical Society
Language eng
Subject 2600 Mathematics
2604 Applied Mathematics
Formatted 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.
Keyword Hyperbolic 3-manifold
Parameter space
Thurston's gluing equations
Triangulation
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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