On Properties of Expansive Group Actions

TL;DR

This paper investigates the properties of expansive group actions on metric and topological spaces, exploring their relationships, conditions, and introducing orbit expansivity for better characterization.

Contribution

It introduces orbit expansivity for group actions and analyzes the relationship between subgroup and group expansivity, including counterexamples and conditions.

Findings

Relation between subgroup and group expansivity established

Counterexamples highlight necessity of hypotheses

Orbit expansivity characterizes expansive actions

Abstract

We study several properties of expansive group actions on metric spaces and obtain relation between expansivity for subgroup and group actions. Through counter examples necessity of hypothesis are justified. We also study expansivity of covering maps. Further, we define orbit expansivity for group actions on topological spaces and use it to characterize expansive action.