Patches covering a sphere and a torus. Wilson loop operators are calculated along the red arrows. (a) Sphere covered with three patches which overlap on ϕ = 0, ϕ = π/2, and ϕ = π. (b) Torus covered with four patches. ϕ and θ are 2π-periodic. Transition functions are taken to be nontrivial only over θ = 0 and ϕ = 0 lines. Figures are adopted from the supplemental materials in Ref. [7].