The fundamentals of cubical isometry groups

TL;DR

This paper develops the foundational theory of cubical isometry groups as totally disconnected, locally compact groups, focusing on their local actions and explicit constructions, with generalizations for future applications.

Contribution

It introduces a comprehensive framework for understanding cubical isometry groups, generalizing previous results and emphasizing their local action determination.

Findings

Cubical isometry groups are totally disconnected, locally compact groups.

Local actions determine cubical isometries.

Framework enables explicit constructions of isometry groups.

Abstract

We develop the fundamental theory to study cubical isometry groups as totally disconnected, locally compact groups. We show how cubical isometries are determined by their local actions and how this can be applied in explicit constructions. These results are closely related to some of the authors recent work on cubical isometries. We reformulate and generalize these previous results in a way that is necessary and more suited for upcoming applications.