On the space of subgroups of Baumslag-Solitar groups II: High
transitivity
Damien Gaboriau, François Le Maître and Yves Stalder
Preprint
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arXiv: https://arxiv.org/abs/2410.23224
Abstract
We continue our study of the perfect kernel of the space of
transitive actions of Baumslag-Solitar groups by investigating high
transitivity. We show that actions of finite phenotype are never
highly transitive, except when the phenotype is $1$, in which case
high transitivity is actually generic. In infinite phenotype, high
transitivity is generic, except when |m|=|n| where it is empty. We
also reinforce the dynamical properties of the action by conjugation
on the perfect kernel that we had established in our first paper,
replacing topological transitivity by high topological transitivity.