Equivariant Movability of Topological Groups

TL;DR

This paper explores the concept of equivariant movability in topological groups, establishing a key characterization that a second countable group is Lie if and only if it exhibits this property.

Contribution

It provides a new characterization of Lie groups among second countable topological groups using the concept of equivariant movability.

Findings

A second countable group is Lie if and only if it is equivariantly movable.

The study advances understanding of the relationship between group structure and topological properties.

It develops the theory of equivariant movability for topological groups.

Abstract

The equivariant movability of topological spaces with an action of a given topological group $G$ is considered. In particular, the equivariant movability of topological groups is studied. It is proved that a second countable group $G$ is Lie if and only if it is equivariantly movable.