Gluing equations for PGL(n,C)-representations of 3-manifolds
Geometric Topology
2015-07-17 v1
Abstract
In a previous paper, we parametrized boundary-unipotent representations of a 3-manifold group into SL(n,C) using Ptolemy coordinates, which were inspired by A-coordinates on higher Teichm\"uller space due to Fock and Goncharov. In this paper, we parametrize representations into PGL(n,C) using shape coordinates which are a 3-dimensional analogue of Fock and Goncharov's X-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.
Keywords
Cite
@article{arxiv.1207.6711,
title = {Gluing equations for PGL(n,C)-representations of 3-manifolds},
author = {Stavros Garoufalidis and Matthias Goerner and Christian K. Zickert},
journal= {arXiv preprint arXiv:1207.6711},
year = {2015}
}
Comments
47 pages, 28 figures