Dimension Groups and Dynamical Systems

TL;DR

This paper explores the relationship between topological dynamical systems and their associated dimension groups, focusing on minimal systems like substitution shifts, Sturmian shifts, and interval exchange shifts.

Contribution

It provides a detailed description of the link between dynamical systems and dimension groups, especially for minimal systems and substitution shifts.

Findings

Characterization of dimension groups for Sturmian shifts

Analysis of interval exchange shifts

Framework for linking dynamical systems with algebraic invariants

Abstract

We give a description of the link between topological dynamical systems and their dimension groups. The focus is on minimal systems and, in particular, on substitution shifts. We describe in detail the various classes of systems including Sturmian shifts and interval exchange shifts. This is a preliminary version of a book which will be published by Cambridge University Press. Any comments are of course welcome.