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2019 On the homotopy types of $\mathrm{Sp}(n)$ gauge groups
Daisuke Kishimoto, Akira Kono
Algebr. Geom. Topol. 19(1): 491-502 (2019). DOI: 10.2140/agt.2019.19.491

## 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 ${\left(p-1\right)}^{2}+1\ge 2n$.

## Citation

Daisuke Kishimoto. Akira Kono. "On the homotopy types of $\mathrm{Sp}(n)$ gauge groups." Algebr. Geom. Topol. 19 (1) 491 - 502, 2019. https://doi.org/10.2140/agt.2019.19.491

## Information

Received: 26 April 2018; Revised: 9 July 2018; Accepted: 3 September 2018; Published: 2019
First available in Project Euclid: 12 February 2019

zbMATH: 07053581
MathSciNet: MR3910588
Digital Object Identifier: 10.2140/agt.2019.19.491

Subjects:
Primary: 54C35‎, 55P15
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