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Homotopy types of gauge groups of \\(\\mathrm{PU}(p)\\)-bundles over spheres
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Homotopy types of gauge groups of \\(\\mathrm{PU}(p)\\)-bundles over spheres
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Paper
Homotopy types of gauge groups of \\(\\mathrm{PU}(p)\\)-bundles over spheres
2020
Overview
We examine the relation between the gauge groups of \\(\\mathrm{SU}(n)\\)- and \\(\\mathrm{PU}(n)\\)-bundles over \\(S^{2i}\\), with \\(2\\leq i\\leq n\\), particularly when \\(n\\) is a prime. As special cases, for \\(\\mathrm{PU}(5)\\)-bundles over \\(S^4\\), we show that there is a rational or \\(p\\)-local equivalence \\(\\mathcal{G}_{2,k}\\simeq_{(p)}\\mathcal{G}_{2,l}\\) for any prime \\(p\\) if, and only if, \\((120,k)=(120,l)\\), while for \\(\\mathrm{PU}(3)\\)-bundles over \\(S^6\\) there is an integral equivalence \\(\\mathcal{G}_{3,k}\\simeq\\mathcal{G}_{3,l}\\) if, and only if, \\((120,k)=(120,l)\\).
Publisher
Cornell University Library, arXiv.org
Subject
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