Equivariant CW-complexes homotopy equivalent to spheres: a survey

TL;DR

This survey reviews finite group actions on CW-complexes, focusing on those homotopy equivalent to spheres, summarizing extensive literature and the authors' joint work in this area.

Contribution

It provides a concise overview of the theory of finite group actions on CW-complexes homotopy equivalent to spheres, highlighting recent developments and applications.

Findings

Summarizes key results on finite G-CW complexes homotopy equivalent to spheres.

Highlights applications of group actions in topology and geometry.

Provides an overview of the literature and open problems in the area.

Abstract

This is a survey about finite group actions on CW-complexes and related topics, primarily based on our joint work. The main applications are to finite $G$-CW-complexes which are homotopy equivalent to spheres. We have tried to give a fairly short overview of the extensive literature in this area, and we apologize in advance for our oversights and omissions.