#### Volume 19, issue 1 (2019)

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On the homotopy types of $\mathrm{Sp}(n)$ gauge groups

### Daisuke Kishimoto and Akira Kono

Algebraic & Geometric Topology 19 (2019) 491–502
##### Abstract

Let ${\mathsc{G}}_{k,n}$ be the gauge group of the principal $Sp\left(n\right)$–bundle over ${S}^{4}$ corresponding to $k\in ℤ\cong {\pi }_{3}\left(Sp\left(n\right)\right)$. We refine the result of Sutherland on the homotopy types of ${\mathsc{G}}_{k,n}$ and relate it to the order of a certain Samelson product in $Sp\left(n\right)$. Then we classify the $p$–local homotopy types of ${\mathsc{G}}_{k,n}$ for ${\left(p-1\right)}^{2}+1\ge 2n$.

##### Keywords
gauge group, homotopy type, unstable K–theory
##### Mathematical Subject Classification 2010
Primary: 54C35, 55P15