Null actions and RIM non-open extensions of strongly proximal actions

TL;DR

The paper constructs a specific type of minimal null action for nonabelian free groups, which extends an effective strongly proximal action in a non-open way, addressing a question posed by Glasner.

Contribution

It demonstrates the existence of such actions for finitely generated nonabelian free groups, providing new insights into their dynamical properties.

Findings

Existence of minimal null actions as RIM non-open extensions

Extension of effective strongly proximal actions

Addresses Glasner's question on group actions

Abstract

Answering a question of Glasner, we show that any finitely generated nonabelian free group has a minimal null action which is a RIM non-open extension of an effective strongly proximal action.