The Ptolemy field of $3$-manifold-representations

Stavros Garoufalidis; Matthias Goerner; Christian K. Zickert

doi:10.2140/agt.2015.15.371

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arXiv · 1401.5542

The Ptolemy field of $3$-manifold-representations

Stavros Garoufalidis·Matthias Goerner·Christian K. Zickert

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Abstract

The Ptolemy coordinates for boundary-unipotent SL(n,C)-representations of a 3-manifold group were introduced in Garoufalidis-Thurston-Zickert inspired by the A-coordinates on higher Teichmüller space due to Fock and Goncharov. In this paper, we define the Ptolemy field of a (generic) PSL(2,\C)-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.

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Stavros Garoufalidis, Matthias Goerner, Christian K. Zickert. 2014-01-22. The Ptolemy field of $3$-manifold-representations. https://doi.org/10.2140/agt.2015.15.371

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