Rokhlin's theorem

In 4-dimensional topology, a branch of mathematics, Rokhlin's theorem states that if a smooth, orientable, closed 4-manifold M has a spin structure (or, equivalently, the second Stiefel–Whitney class ${\displaystyle w_{2}(M)}$ vanishes), then the signature of its intersection form, a quadratic form on the second cohomology group ${\displaystyle H^{2}(M)}$, is divisible by 16. The theorem is named for Vladimir Rokhlin, who proved it in 1952.