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