Topological Full Groups

TL;DR

This survey introduces topological full groups, exploring their origins in dynamical systems and their significant impact on group theory, highlighting their theoretical background, dynamical significance, and group properties.

Contribution

It provides a comprehensive overview of topological full groups, emphasizing their development, importance in dynamics, and recent group-theoretic insights.

Findings

Topological full groups connect dynamical systems with group theory.

They exhibit rich algebraic structures influenced by dynamical properties.

Recent research reveals new classifications and properties of these groups.

Abstract

Topological full groups originated from the theory of topological dynamical systems and have been having considerable impact on group theory in recent years. This text represents an introduction/survey on topological full groups. After development of the theoretical and historical background, it gives an account of their significance in topological dynamics and discusses their group theoretical aspects.