A note on homotopy types of connected components of Map(S[4], B SU(2))

概要

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Gottlieb has shown that connected components of Map(S[4], B SU(2)) are the classifying spaces of gauge groups of principal SU(2)-bundles over S[4]. Tsukuda has investigated the homotopy types of connected components of Map(S[4], B SU(2)). But unfortunately, his proof is not complete for p=2. In this paper, we give a complete proof. Moreover, we investigate the further divisibility of ϵi defined in Tsukuda’s paper. We apply this to classification problem of gauge groups as An-spaces.