On groups acting on contractible spaces with stabilizers of prime power order

TL;DR

This paper investigates how discrete groups act on contractible spaces with specific stabilizer subgroup conditions, comparing classifying spaces, hierarchies, and cohomology relative to prime power and finite subgroups.

Contribution

It provides a comparative analysis of classifying spaces, hierarchies, and cohomology for groups with stabilizers of prime power order versus finite subgroups.

Findings

Comparison of classifying spaces for different stabilizer families

Analysis of Kropholler hierarchies based on these families

Group cohomology relative to prime power and finite stabilizer families

Abstract

We study actions of discrete groups on contractible topological spaces in which either (1) all stabilizers lie in the family of subgroups of prime power order or (2) all stabilizers lie in the family of finite subgroups. We compare the classifying spaces for actions with stabilizers in these two families, the Kropholler hierarchies build on these two families, and group cohomology relative to these two families.