Dynamics on the perfect kernel of higher rank generalized Baumslag-Solitar groups

2025/09/30 by Sasha Bontemps, Bontemps, Sasha
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Geometric and Algebraic Topology #Quantum chaos and dynamical systems #math.DS #math.GR

paper · pdf · doi:10.48550/arxiv.2509.26143

openalex publication_date 2025/09/30 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/30

Abstract

In this article, we study the space of subgroups of non-amenable generalized Baumslag-Solitar groups (GBS groups) of rank d, that is, groups acting cocompactly on an oriented tree with vertex and edge stabilizers isomorphic to ℤ^d. Our results generalize the study of Baumslag-Solitar groups, and of GBS groups of rank 1. We give an explicit description of the perfect kernel of a non-amenable GBS group G of rank d and show the existence of a partition of the perfect kernel into a countably infinite set of pieces which are invariant under the action by conjugation of G, and such that each piece contains a dense orbit.

Citations

• Perfect kernel of generalized Baumslag-Solitar groups
• On the space of subgroups of Baumslag-Solitar groups II: High transitivity
• Separability properties of higher-rank GBS groups
• Perfect kernel and dynamics: from Bass-Serre theory to hyperbolic groups
• On the space of subgroups of Baumslag-Solitar groups I: perfect kernel and phenotype
• Generalised Baumslag-Solitar groups and Hierarchically Hyperbolic Groups
• The large scale geometry of the higher Baumslag-Solitar groups

Related

• Perfect kernel of generalized Baumslag-Solitar groups
• On the space of subgroups of Baumslag-Solitar groups I: perfect kernel and phenotype
• The large scale geometry of the higher Baumslag-Solitar groups
• On the space of subgroups of Baumslag-Solitar groups II: High transitivity
• Fixed subgroups of generalised Baumslag-Solitar groups