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The Ptolemy field of
$3$–manifold representations
Stavros Garoufalidis, Matthias Goerner and Christian K Zickert |
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Algebraic & Geometric Topology 15 (2015) 371–397
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Abstract |
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The Ptolemy coordinates for boundary-unipotent –representations of a –manifold group were introduced by Garoufalidis, Thurston and Zickert [arXiv:1111.2828] inspired by the –coordinates on higher Teichmüller space due to Fock and Goncharov. We define the Ptolemy field of a (generic) -representation and prove that it coincides with the trace field of the representation. This gives an efficient algorithm to compute the trace field of a cusped hyperbolic manifold. |
Keywords
Ptolemy coordinates, trace field, SnapPy, $3$–manifold
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Mathematical Subject Classification 2010
Primary: 57N10
Secondary: 57M27
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References |
Publication
Received: 21 January 2014
Revised: 9 May 2014
Accepted: 7 July 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 United States |
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| http://www2.math.umd.edu/~zickert | |
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