Boomerang subgroups

Abstract: Given a locally compact group, its set of closed subgroups can be endowed with a compact, Hausdorff topology. With this topology, it is called the Chabauty space of the group. Every group acts on its Chabauty space via conjugation. This action has connections to rigidity theory, Margulis' normal subgroup theorem and measure preserving actions of the group via so-called Invariant Random Subgroups (IRS). I will give a gentle introduction into Chabauty spaces and IRS and state a few classical results. I will define boomerang subgroups and explain how special cases of the classical results can be proven via them. Based on joint work with Yair Glasner.

group theory

Audience: researchers in the topic

Groups in Galway 2024