The homotopy types of compact Lie groups
type: Item
instance of: scholarly article
title: The homotopy types of compact Lie groups
zbMATH Open document ID: 0581.55005
DOI: 10.1007/BF02772955
author: J. R. Hubbuck
author: Richard Kane
published in: Israel Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: A homotopy theoretic and homological proof is given to a theorem of H. Scheerer: If two compact simply connected Lie groups are homotopy equivalent they are isomorphic. Both the original and the present proofs make use of the known list of the simple Lie groups. These are distinguishable by their mod 2 cohomology. However, distinct products of simple groups may produce mod p equivalent spaces. This paper proves that the above phenomena cannot occur simultaneously at the primes 2 and 3. Thus, two simply connected compact Lie groups which are mod 2 and mod 3 equivalent are isomorphic.
Mathematics Subject Classification ID: 55P15
Mathematics Subject Classification ID: 55S10
Mathematics Subject Classification ID: 57T10
zbMATH DE Number: 3929942
zbMATH Keywords: homotopy equivalent connected Lie groups
zbMATH Keywords: p-localization
zbMATH Keywords: Steenrod squares
zbMATH Keywords: mod 2 cohomology
zbMATH Keywords: compact Lie groups which are mod 2 and mod 3 equivalent
Wikidata QID: Q115391660
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02772955
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description: scientific article; zbMATH DE number 3929942