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arXiv · 1803.06477

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

Daisuke Kishimoto·Akira Kono
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Abstract

Let $\mathcal{G}_{k,n}$ be the gauge group of the principal $\mathrm{Sp}(n)$-bundle over $S^4$ corresponding to $k\in\mathbb{Z}\cong\pi_3(\mathrm{Sp}(n))$. We refine the result of Sutherland on the homotopy types of $\mathcal{G}_{k,n}$ and relate it with the order of a certain Samelson product in $\mathrm{Sp}(n)$. Then we classify the $p$-local homotopy types of $\mathcal{G}_{k,n}$ for $(p-1)^2+1\ge 2n$.

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Daisuke Kishimoto, Akira Kono. 2018-03-17. On the homotopy types of $\mathrm{Sp}(n)$ gauge groups. https://doi.org/10.2140/agt.2019.19.491

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