Homotopy decomposition of classifying spaces via elementary Abelian subgroups
type: Item
instance of: scholarly article
title: Homotopy decomposition of classifying spaces via elementary Abelian subgroups
zbMATH Open document ID: 0754.55014
DOI: 10.1016/0040-9383(92)90065-P
author: Stefan Jackowski
author: James E. McClure
published in: Topology
publication date: 1992-09-26T00:00:00Z
review text: In this paper the authors show that the classifying space of any compact Lie group \(G\) can be reconstructed up to homotopy (i.e., as a homotopy colimit) from the classifying spaces of the centralizers of the nontrivial elementary abelian subgroups of \(G\). One of the steps in the argument is to show that \(H^*BG\) is the inverse limit of \(H^*BC_ G(E)\) as \(E\) ranges over the nontrivial elementary abelian subgroups of \(G\); this supplements a result of \textit{D. Quillen} [Ann. Math., II. Ser. 94, 549-572 (1971; Zbl 0247.57013)] according to which \(H^*BG\) is \(\mathcal F\)-isomorphic to the inverse limit of \(H^*BE\). The main result has been generalized to certain spaces which are not classifying spaces and proved by a different argument in \textit{W. G. Dwyer} and \textit{C. W. Wilkerson's} paper ``A cohomology decomposition theorem'' [Topology 31, No. 2, 433-443 (1992)].
Mathematics Subject Classification ID: 55R35
Mathematics Subject Classification ID: 55T10
zbMATH DE Number: 54633
zbMATH Keywords: spectral sequences
zbMATH Keywords: classifying space compact Lie group
zbMATH Keywords: homotopy colimit
zbMATH Keywords: classifying spaces of the centralizers of the nontrivial elementary abelian subgroups
Wikidata QID: Q106627463
MaRDI profile type: Publication
full work available at URL: 0040-9383(92)90065-p
OpenAlex ID: W2013056831
description: scientific article; zbMATH DE number 54633