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.
All Science Journal Classification (ASJC) codes
- Geometry and Topology