Subgroup mixing in Baumslag-Solitar groups
Abstract
In this article, we contribute to the study of the dynamics induced by the conjugation action on the space of subgroups of Baumslag-Solitar groups BS(m,n), via the mixing properties of elements asymptotically produced by suitable random walks on the group. In an acylindrically hyperbolic context, the authors of [HMO] demonstrated strong mixing situations, namely topological mu-mixing, a strengthening of high topological transitivity. Regarding non-metabelian and non-unimodular BS(m,n), we exhibit here a radically different situation on each of the pieces except one of the partition introduced in [CGLMS22] (although it is highly topologically transitive on each piece). On the other hand, when BS(m,n) is unimodular, we demonstrate the topological mu-mixing character on each of the pieces.
Keywords
Cite
@article{arxiv.2505.07667,
title = {Subgroup mixing in Baumslag-Solitar groups},
author = {Sasha Bontemps},
journal= {arXiv preprint arXiv:2505.07667},
year = {2026}
}
Comments
An overly hasty argument that required a detailed justification was found in the proof of Theorem 1.2. In order to clearly highlight the arguments, a new subsection 'escaping the compact core' and several detailed lemmas have been added