Group Actions and Covering Maps in the Uniform Category

TL;DR

This paper explores the relationship between group actions and covering maps in uniform spaces, introduces generalized uniform covering maps, and applies these concepts to analyze Prajs' homogeneous curve with unique connectivity properties.

Contribution

It characterizes when generalized uniform covering maps are induced by group actions and applies this to a notable example of a homogeneous curve.

Findings

Characterization of group-induced covering maps in uniform spaces

Introduction of generalized uniform covering maps

Analysis of Prajs' homogeneous curve

Abstract

In Rips Complexes and Covers in the Uniform Category (arXiv:0706.3937) we define, following James, covering maps of uniform spaces and introduce the concept of generalized uniform covering maps. In this paper we investigate when these covering maps are induced by group actions. Also, as an application of our results we present an exposition of Prajs' homogeneous curve that is path-connected but not locally connected.