The homotopy types of PU(3)– and PSp(2)–gauge groups

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

doi:10.2140/agt.2016.16.1813

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

Sho Hasui, Daisuke Kishimoto, Akira Kono and Takashi Sato

Algebraic & Geometric Topology 16 (2016) 1813–1825

DOI: 10.2140/agt.2016.16.1813

Abstract

Let $G$ be a compact connected simple Lie group. Any principal $G$ –bundle over $S^{4}$ is classified by an integer $k \in ℤ ≅ π_{3} (G)$ , and we denote the corresponding gauge group by $G_{k} (G)$ . We prove that $G_{k} (PU (3)) ≃ G_{ℓ} (PU (3))$ if and only if $(24, k) = (24, ℓ)$ , and $G_{k} (PSp (2)) ≃_{(p)} G_{ℓ} (PSp (2))$ for any prime $p$ if and only if $(40, k) = (40, ℓ)$ , where $(m, n)$ is the gcd of integers $m, n$ .

Keywords

gauge group, Samelson product

Mathematical Subject Classification 2010

Primary: 55P35

Secondary: 55Q15

References

Publication

Received: 23 June 2015

Revised: 29 September 2015

Accepted: 11 December 2015

Published: 1 July 2016

Authors

Sho Hasui
Department of Mathematics Kyoto University Kyoto 606-8502 Japan

Daisuke Kishimoto
Department of Mathematics Kyoto University Kyoto 606-8502 Japan

Akira Kono
Department of Mathematical Science, Faculty of Science and Engineering Doshisha University Kyoto 610-0394 Japan

Takashi Sato
Department of Mathematics Kyoto University Kyoto 606-8502 Japan

Volume 16, issue 3 (2016)