The fundamentals of cubical 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.