Recognition and constructive membership for discrete subgroups of SL₂(ℝ)

2024/10/23 by Ari Markowitz, Markowitz, Ari
Mathematics · #Finite Group Theory Research #Advanced Algebra and Geometry #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2410.18315

Abstract

We provide algorithms to decide whether a finitely generated subgroup of SL₂(ℝ) is discrete, solve the constructive membership problem for finitely generated discrete subgroups of SL₂(ℝ), and compute a fundamental domain for a finitely generated Fuchsian group. These algorithms have been implemented in Magma for groups defined over real algebraic number fields.

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