class S（数学理论）

class S理论的对偶群是moduli space的基本群与证明

The punctures on the z plane are now associated to the factors of the flavor group. The moduli space of a sphere with n＋3 distinguished punctures M'ₙ₊₃，₀ is a cover of the gauge moduli space Mₙ₊₃，₀. The S-duality group π₁(Mₙ₊₃，₀) can be factored as the semi-direct product

0 → π₁(M'＋₃，₀) → π₁(Mₙ₊₃，₀) → S → 0 (2.19)

The quotient S acts as the permutation group on the punctures，i.e.on factors of the flavor group.