The type of the classifying space for a family of subgroups
type: Item
instance of: scholarly article
title: The type of the classifying space for a family of subgroups
zbMATH Open document ID: 0955.55009
DOI: 10.1016/S0022-4049(98)90173-6
published in: Journal of Pure and Applied Algebra
publication date: 2001-02-22T00:00:00Z
review text: Given a group \(\Gamma\), it is a classical problem to determine whether \(\Gamma\) can act freely and preserving cells on some contractible CW-space \(E \Gamma\) whose orbit space is finite, resp. finite dimensional, resp. of finite type. More generally, the author asks if there is a CW-space \({\mathcal E}\Gamma\) on which \(\Gamma\) acts with finite stabilizer groups and contractible fixed point sets and whose orbit space is finite, resp. finite dimensional, resp. of finite type. He gives a necessary condition for the existence of such \({\mathcal E}\Gamma\) such that the fixed point sets have a prescribed dimension. He also shows that this condition is sufficient whenever the length of descending sequences of finite subgroups in \(\Gamma\) is bounded. The existence question of \({\mathcal E}\Gamma\) such that \({\mathcal E}\Gamma/\Gamma\) is finite or of finite type is considered in several settings. The paper closes with a list of interesting open problems on this topic.
Mathematics Subject Classification ID: 55R35
Mathematics Subject Classification ID: 57S99
zbMATH DE Number: 1474722
zbMATH Keywords: group action
author: Wolfgang Lück
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1474722