2018/06/22 by Kechris, Alexander S., Quorning, Vibeke
#Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)
paper · doi:10.48550/arxiv.1806.08590
In this paper we develop a co-induction operation which transforms an invariant random subgroup of a group into an invariant random subgroup of a larger group. We use this operation to construct new continuum size families of non-atomic, weakly mixing invariant random subgroups of certain classes of wreath products, HNN-extensions and free products with amalgamation. By use of small cancellation theory, we also construct a new continuum size family of non-atomic invariant random subgroups of \mathbbF2 which are all invariant and weakly mixing with respect to the action of Aut(\mathbbF2). Moreover, for amenable groups Γ≤ Δ, we obtain that the standard co-induction operation from the space of weak equivalence classes of Γ to the space of weak equivalence classes of Δ is continuous if and only if [Δ:Γ]