Algebraic & Geometric Topology

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

Abstract

Let $G k , n$ be the gauge group of the principal $Sp ( n )$–bundle over $S 4$ corresponding to $k ∈ ℤ ≅ π 3 ( Sp ( n ) )$. We refine the result of Sutherland on the homotopy types of $G k , n$ and relate it to the order of a certain Samelson product in $Sp ( n )$. Then we classify the $p$–local homotopy types of $G k , n$ for $( p − 1 ) 2 + 1 ≥ 2 n$.

Article information

Source
Algebr. Geom. Topol., Volume 19, Number 1 (2019), 491-502.

Dates
Revised: 9 July 2018
Accepted: 3 September 2018
First available in Project Euclid: 12 February 2019

https://projecteuclid.org/euclid.agt/1549940440

Digital Object Identifier
doi:10.2140/agt.2019.19.491

Mathematical Reviews number (MathSciNet)
MR3910588

Zentralblatt MATH identifier
07053581

Citation

Kishimoto, Daisuke; Kono, Akira. On the homotopy types of $\mathrm{Sp}(n)$ gauge groups. Algebr. Geom. Topol. 19 (2019), no. 1, 491--502. doi:10.2140/agt.2019.19.491. https://projecteuclid.org/euclid.agt/1549940440