Work

Dynamics on the Perfect Kernel of Non-amenable Higher-rank Generalized Baumslag-solitar Groups

Year: 2026

Type: article

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 $\mathbb {Z}^d$ double struck upper Z Superscript d . Our results generalize the study of Baumslag-Solitar groups, and of GBS groups of rank 1 $1$ 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 that are invariant under the action by conjugation of G , and such that each piece contains a dense orbit.

Source: Journal of the Institute of Mathematics of Jussieu

DOI: 10.1017/s147474802610200x

Author: Sasha Bontemps

Institution: École Normale Supérieure de Lyon

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funder: École Normale Supérieure de Lyon