The structure of limit groups over hyperbolic groups

2016/03/23 by Groves, Daniel, Wilton, Henry · 1 citation
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1603.07187

Abstract

Let Γ be a torsion-free hyperbolic group. We study Γ--limit groups which, unlike the fundamental case in which Γ is free, may not be finitely presentable or geometrically tractable. We define model Γ--limit groups, which always have good geometric properties (in particular, they are always relatively hyperbolic). Given a strict resolution of an arbitrary Γ--limit group L, we canonically construct a strict resolution of a model Γ--limit group, which encodes all homomorphisms L→ Γ that factor through the given resolution. We propose this as the correct framework in which to study Γ--limit groups algorithmically. We enumerate all Γ--limit groups in this framework.

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• Algebraic groups over free and hyperbolic groups

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