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Gluing equations for
$\mathrm{PGL}(n,\mathbb{C})$–representations of
$3$–manifolds
Stavros Garoufalidis, Matthias Goerner and Christian K Zickert |
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Algebraic & Geometric Topology 15 (2015) 565–622
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Abstract |
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Garoufalidis, Thurston and Zickert parametrized boundary-unipotent representations of a 3–manifold group into using Ptolemy coordinates, which were inspired by –coordinates on higher Teichmüller space due to Fock and Goncharov. We parametrize representations into using shape coordinates, which are a –dimensional analogue of Fock and Goncharov’s –coordinates. These coordinates satisfy equations generalizing Thurston’s gluing equations. These equations are of Neumann–Zagier type and satisfy symplectic relations with applications in quantum topology. We also explore a duality between the Ptolemy coordinates and the shape coordinates. |
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Keywords
generalized gluing equations, shape coordinates, Ptolemy
coordinates, Neumann–Zagier datum
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Mathematical Subject Classification 2010
Primary: 57M27, 57N10
Secondary: 53D50
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References |
Publication
Received: 7 November 2014
Accepted: 13 December 2014
Published: 23 March 2015
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Authors |
| Stavros Garoufalidis | |
| School of Mathematics Georgia Institute of Technology 686 Cherry Street Atlanta, GA 30332-0160 USA |
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| http://www.math.gatech.edu/~stavros | |
| Matthias Goerner | |
| Pixar Animation Studios 1200 Park Avenue Emeryville, CA 94608 USA |
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| http://www.unhyperbolic.org/ | |
| Christian K Zickert | |
| Department of Mathematics University of Maryland College Park, MD 20742-4015 USA |
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| http://www2.math.umd.edu/~zickert | |
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