On Bredon (Co-)Homological Dimensions of Groups

TL;DR

This paper investigates the minimal dimensions of classifying spaces for groups with virtually cyclic stabilizers, providing insights into their Bredon (co-)homological dimensions.

Contribution

It offers a detailed analysis of Bredon (co-)homological dimensions for groups, focusing on classifying spaces with virtually cyclic stabilizers, advancing understanding in this area.

Findings

Determined minimal dimensions for classifying spaces with specific stabilizers.

Analyzed Bredon (co-)homological dimensions for various groups.

Provided corrected and extended results from the author's PhD thesis.

Abstract

This is a revised version of the author's PhD thesis, including the corrections by the examiners. It also includes a few additional small corrections. In this thesis the objects of study are classifying spaces of groups with stabilisers in a given family of subgroups. Given a group G and a family of subgroups we study the minimal dimension a classifying space can have. We focus on classifying spaces with virtually cyclic stabilisers.