Homotopy nilpotent Lie groups have no torsion in homology
type: Item
instance of: scholarly article
title: Homotopy nilpotent Lie groups have no torsion in homology
zbMATH Open document ID: 0880.22005
DOI: 10.1007/BF02678205
published in: Manuscripta Mathematica
publication date: 1998-01-12T00:00:00Z
full work available at URL: https://eudml.org/doc/156275
review text: An \(H\)-space \(X\) is homotopy nilpotent if and only if the groups \([-,X]\) are always nilpotent. The author shows that if \(G\) is a compact connected Lie group that has \(p \)-torsion in homology, then \(G\) localized at \(p\) is not homotopy nilpotent. This implies that a connected Lie group is homotopy nilpotent if and only if it has no torsion in homology. Also proven is the fact that the localization \(G_{(p)}\) is homotopy nilpotent if and only if \(H(G; \mathbb{Z}_{(p)})\) is torsion free. The if-part is due to M. Hopkins.
Mathematics Subject Classification ID: 22E41
Mathematics Subject Classification ID: 55Q05
Mathematics Subject Classification ID: 55P60
Mathematics Subject Classification ID: 57T15
zbMATH DE Number: 1038277
zbMATH Keywords: localization
zbMATH Keywords: Morava \(K\)-theory
zbMATH Keywords: spectral sequence
zbMATH Keywords: homotopy nilpotent
zbMATH Keywords: Lie group
zbMATH Keywords: homology
author: Vidhyanath K. Rao
reviewed by: Daniel H. Gottlieb
MaRDI profile type: Publication
Wikidata QID: Q115391886
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description: scientific article; zbMATH DE number 1038277