Fundamental regions for non-isometric group actions

Abstract

We generalise results about isometric group actions on metric spaces and their fundamental regions to the context of merely continuous group actions. In particular, we obtain results that yield the relative compactness of a fundamental region for a cocompact group action. As a consequence, we obtain a criterion for a cocompact cyclic group of semi-Riemannian homotheties to be inessential.

In v2 the notion of a `strongly locally finite region' in Definition 2.1 replaces the notion of a `finitely self adjacent fundamental region' from v1. As a result, v2 is completely rewritten. See Remark 2.3 for further explanation