Minimal flows with arbitrary centralizer

TL;DR

This paper constructs minimal, free Cantor flows for any countable group G, embedding any other countable group H into the automorphism group, thus exploring the structure of group actions on topological dynamics.

Contribution

It introduces a method to realize any countable group H as automorphisms of a minimal free G-flow for any infinite countable group G, expanding understanding of group actions in dynamics.

Findings

Existence of minimal free G-flows with arbitrary automorphism groups

Embedding of any countable group H into automorphisms of the constructed flow

Generalization of automorphism groups in topological dynamics

Abstract

Given any pair of countable groups $G$ and $H$ with $G$ infinite, we construct a minimal, free, Cantor $G$-flow $X$ so that $H$ embeds into the group of automorphisms of $X$.