## Algebraic & Geometric Topology

### The homotopy types of $\mathrm{PU}(3)$– and $\mathrm{PSp}(2)$–gauge groups

#### Abstract

Let $G$ be a compact connected simple Lie group. Any principal $G$–bundle over $S4$ is classified by an integer $k ∈ ℤ≅π3(G)$, and we denote the corresponding gauge group by $Gk(G)$. We prove that $Gk(PU(3)) ≃Gℓ(PU(3))$ if and only if $(24,k) = (24,ℓ)$, and $Gk(PSp(2)) ≃(p)Gℓ(PSp(2))$ for any prime $p$ if and only if $(40,k) = (40,ℓ)$, where $(m,n)$ is the gcd of integers $m,n$.

#### Article information

Source
Algebr. Geom. Topol., Volume 16, Number 3 (2016), 1813-1825.

Dates
Revised: 29 September 2015
Accepted: 11 December 2015
First available in Project Euclid: 28 November 2017

https://projecteuclid.org/euclid.agt/1511895863

Digital Object Identifier
doi:10.2140/agt.2016.16.1813

Mathematical Reviews number (MathSciNet)
MR3523056

Zentralblatt MATH identifier
1352.55005

Subjects
Primary: 55P35: Loop spaces
Secondary: 55Q15: Whitehead products and generalizations

Keywords
gauge group Samelson product

#### Citation

Hasui, Sho; Kishimoto, Daisuke; Kono, Akira; Sato, Takashi. The homotopy types of $\mathrm{PU}(3)$– and $\mathrm{PSp}(2)$–gauge groups. Algebr. Geom. Topol. 16 (2016), no. 3, 1813--1825. doi:10.2140/agt.2016.16.1813. https://projecteuclid.org/euclid.agt/1511895863