Algebraic & Geometric Topology

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

Sho Hasui, Daisuke Kishimoto, Akira Kono, and Takashi Sato

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

Article information

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

Received: 23 June 2015
Revised: 29 September 2015
Accepted: 11 December 2015
First available in Project Euclid: 28 November 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

gauge group Samelson product


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.

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