Amenability and skew-amenability of actions of topological groups

TL;DR

This paper introduces and investigates the concepts of amenability and skew-amenability for continuous actions of topological groups on compact spaces, focusing on how these properties transfer to subgroups and their implications for universal minimal flows.

Contribution

It defines new notions of amenability and skew-amenability for group actions and explores their properties and applications, especially regarding subgroup inheritance and minimal flows.

Findings

Amenability can pass to certain subgroups under specific conditions.

Skew-amenability provides a broader framework for non-amenable groups.

Applications include understanding universal minimal flows of non-amenable groups.

Abstract

We define and study notions of amenability and skew-amenability of continuous actions of topological groups on compact topological spaces. Our main motivation is the question under what conditions amenability of a topological group passes to a closed subgroup. Other applications include the understanding of the universal minimal flow of various non-amenable groups.