Registry · Theorem
IV.T208
established
formalized
IV.T208 — No Magnetic Monopoles on T²
χ(T²)=0 ⟹ ∇·B=0 identically. No monopole charges on T². Gauss-Bonnet: ∮F = 2πχ(T²) = 0. Electric-magnetic duality: charge = boundary obstruction (nontrivial), monopole = Euler obstruction (zero).