Composition methods and homotopy types of the gauge groups of \(Sp(2)\) and \(SU(3)\)
type: Item
instance of: scholarly article
title: Composition methods and homotopy types of the gauge groups of \(Sp(2)\) and \(SU(3)\)
zbMATH Open document ID: 1155.55001
author: Younggi Choi
author: Yoshihiro Hirato
author: Mamoru Mimura
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2008-11-07T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bbms/1222783089
review text: For a compact connected simple Lie group \(G\), let \(P_k\) denote the principal \(G\)-bundle over \(S^4\) with the topological quantum number \(k\in\mathbb Z=\pi_4(BG)\) and let \({\mathcal G}_k\) be the corresponding gauge group. In this paper the authors study the homotopy types of the gauge group \({\mathcal G}\) for \(G=Sp(2)\) or \(SU(3)\), and compute the low dimensional homotopy sets related to the group \({\mathcal G}\) by using Toda's composition method. As an application, they obtain several sufficient conditions for integers \((k,l)\) under which two gauge groups \({\mathcal G}_k\) and \({\mathcal G}_l\) are homotopy equivalent. Moreover, they give another proof of a theorem concerning the homotopy types of \({\mathcal G}_k\) for \(G=SU(3)\) obtained by Kono-Hamanaka.
reviewed by: Kohhei Yamaguchi
Mathematics Subject Classification ID: 55P15
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 55P10
Mathematics Subject Classification ID: 57T99
zbMATH DE Number: 5363265
zbMATH Keywords: composition method
zbMATH Keywords: gauge group
zbMATH Keywords: homotopy type
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5363265