More on the Kechris-Pestov-Todorcevic correspondence: precompact expansions

TL;DR

This paper extends the Kechris-Pestov-Todorcevic correspondence to handle precompact expansions, simplifying the computation of universal minimal flows in topological dynamics.

Contribution

It introduces modifications to the original [KPT] framework, enabling direct calculations of universal minimal flows without additional adjustments.

Findings

Enhanced the [KPT] framework for precompact expansions

Simplified computation of universal minimal flows

Broadened applicability of the correspondence

Abstract

In 2005, the paper "Fraiss\'e limits, Ramsey theory, and topological dynamics of automorphism groups" [KPT] by Kechris, Pestov and Todorcevic provided a powerful tool to compute an invariant of topological groups known as the universal minimal flow. This immediately led to an explicit representation of this invariant in many concrete cases. However, in some particular situations, the framework of [KPT] does not allow to perform the computation directly, but only after a slight modification of the original argument. The purpose of the present paper is to supplement [KPT] in order to avoid that twist and to make it adapted for further applications.