Rank 1 character varieties of finitely presented groups
Abstract
Let X(F,G) be the G-character variety of F where G is a rank 1 complex affine algebraic group and F is a finitely presentable discrete group. We describe an algorithm, which we implement in Mathematica, SageMath, and in Python, that takes a finite presentation for F and produces a finite presentation of the coordinate ring of X(F,G). We also provide a new description of the defining relations and local parameters of the coordinate ring when F is free. Although the theorems used to create the algorithm are not new, we hope that as a well-referenced exposition with a companion computer program it will be useful for computation and experimentation with these moduli spaces.
Keywords
Cite
@article{arxiv.1703.08241,
title = {Rank 1 character varieties of finitely presented groups},
author = {Caleb Ashley and Jean-Philippe Burelle and Sean Lawton},
journal= {arXiv preprint arXiv:1703.08241},
year = {2018}
}
Comments
30 pages, Mathematica program at http://math.gmu.edu/~slawton3/trace-identities.nb, SageMath program at http://math.gmu.edu/~slawton3/Main.sagews, Python program at http://math.gmu.edu/~slawton3/charvars.py, accepted for publication at Geometriae Dedicata