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

Sho Hasui; Daisuke Kishimoto; Akira Kono; Takashi Sato

doi:10.2140/agt.2016.16.1813

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

Sho Hasui, Daisuke Kishimoto, Akira Kono, Takashi Sato

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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 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.

Original language	English
Pages (from-to)	1813-1825
Number of pages	13
Journal	Algebraic and Geometric Topology
Volume	16
Issue number	3
DOIs	https://doi.org/10.2140/agt.2016.16.1813
Publication status	Published - Jul 1 2016
Externally published	Yes

All Science Journal Classification (ASJC) codes

Geometry and Topology

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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.",

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AU - Hasui, Sho

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AU - Sato, Takashi

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N2 - 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.

AB - 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.

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

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