The group of self-homotopy classes of SO(4)
type: Item
instance of: scholarly article
title: The group of self-homotopy classes of SO(4)
zbMATH Open document ID: 1032.55011
DOI: 10.1016/S0022-4049(03)00105-1
author: Ōshima Hideaki
published in: Journal of Pure and Applied Algebra
publication date: 2003-11-19T00:00:00Z
review text: Let \({\mathcal H}(G)=[G,G]\) denote the group of homotopy classes of maps of a topological group \(G\) into itself, with group structure induced by that of \(G\). The author considers the case where \(G\) is a compact, connected, semi-simple and non-simple Lie group of rank \(2\), that is \(S^3\times S^3\), \(S^3\times SO(3)\), \(SO(4)\) or \(SO(3)\times SO(3)\). He gives presentations for \({\mathcal H}(G)\) in the cases of \(S^3\times SO(3)\) and \(SO(4)\); results for \(S^3\times S^3\) and certain other low rank Lie groups are already known. He determines the nilpotency of \({\mathcal H}(G)\) in each of the four cases, and shows that \({\mathcal H}(S^3\times SO(3))\) and \({\mathcal H}(SO(4))\) are not isomorphic, even though \(S^3\times SO(3)\) and \(SO(4)\) are homeomorphic.
Mathematics Subject Classification ID: 55Q05
Mathematics Subject Classification ID: 57T99
Mathematics Subject Classification ID: 20F38
zbMATH DE Number: 2005927
zbMATH Keywords: group of homotopy classes of maps
zbMATH Keywords: topological group
reviewed by: John W. Rutter
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2005927