Euler classes and Bredon cohomology for groups with restricted families of finite subgroups

TL;DR

This paper investigates Bredon cohomology for groups with specific finite subgroup families, deriving results on dimensions, Euler classes, and duality properties, especially under p-power index extensions.

Contribution

It provides new formulas for Euler classes and explores duality properties in Bredon cohomology for groups with restricted finite subgroups.

Findings

Formulas for equivariant Euler classes

Results on Bredon cohomology dimensions

Behavior of duality under p-power extensions

Abstract

We explore some of the special features with respect to Bredon cohomology of groups having all its finite subgroups either nilpotent or p-groups or cyclic p-groups. We get some results on dimensions and also a formula for the equivariant Euler class for certain groups. We consider the generalization for Bredon cohomology of the properties of being duality or Poincar\'e duality and study their behavior under p-power index extensions with coefficients in a field of characteristic p.