The Ptolemy field of $3$-manifold-representations
Geometric Topology
2015-07-17 v1
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 Teichm\"{u}ller 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.
Keywords
Cite
@article{arxiv.1401.5542,
title = {The Ptolemy field of $3$-manifold-representations},
author = {Stavros Garoufalidis and Matthias Goerner and Christian K. Zickert},
journal= {arXiv preprint arXiv:1401.5542},
year = {2015}
}
Comments
21 pages, 23 figures