Topological groups: where to from here?

TL;DR

This paper surveys recent developments in the theory of topological groups, focusing on group actions, embeddings, free groups, and large groups like homeomorphism and isometry groups, highlighting future research directions.

Contribution

It provides a comprehensive overview of current trends and future directions in topological group theory, emphasizing areas like group actions and large group structures.

Findings

Identifies key recent advances in topological group theory

Highlights importance of actions on compacta and embeddings

Suggests promising future research directions

Abstract

This is an account of one man's view of the current perspective of theory of topological groups. We survey some recent developments which are, from our viewpoint, indicative of the future directions, concentrating on actions of topological groups on compacta, embeddings of topological groups, free topological groups, and `massive' groups (such as groups of homeomorphisms of compacta and groups of isometries of various metric spaces).