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arXiv · 1703.08241

Rank 1 character varieties of finitely presented groups

Caleb Ashley·Jean-Philippe Burelle·Sean Lawton
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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.

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Caleb Ashley, Jean-Philippe Burelle, Sean Lawton. 2017-03-23. Rank 1 character varieties of finitely presented groups. https://doi.org/10.1007/s10711-017-0281-6

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