On extending actions of groups

TL;DR

This paper addresses the extension of group actions, providing solutions for dense and closed extensions of compact transformation groups and applying these methods to extend equivariant maps and construct equivariant compactifications.

Contribution

It introduces a new method for extending actions of compact groups and applies it to problems of equivariant map extension and compactification construction.

Findings

Dense and closed extension solutions for compact group actions

Method for extending equivariant maps

Construction of equivariant compactifications

Abstract

Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications.