Homotopy types of gauge groups of PU(p)-bundles over spheres

2020/04/10 by Rea, Simon
#55P15 (Primary) #55Q05 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2004.04925

Abstract

We examine the relation between the gauge groups of SU(n)- and PU(n)-bundles over S²ⁱ, with 2≤ i≤ n, particularly when n is a prime. As special cases, for PU(5)-bundles over S⁴, we show that there is a rational or p-local equivalence G_2,k≃_(p)G_2,l for any prime p if, and only if, (120,k)=(120,l), while for PU(3)-bundles over S⁶ there is an integral equivalence G_3,k\simeqG_3,l if, and only if, (120,k)=(120,l).

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