High Quality Content by WIKIPEDIA articles! In 4-dimensional topology, a branch of mathematics, Rokhlin's theorem states that if a smooth, compact 4-manifold M has a spin structure (or, equivalently, the second Stiefel-Whitney class w2(M) vanishes), then the signature of its intersection form, a quadratic form on the second cohomology group H2(M), is divisible by 16. The theorem is named for Vladimir Rokhlin, who proved it in 1952. Rokhlin's theorem can be deduced from the fact that the third stable homotopy group of spheres ?S3 is cyclic of order 24; this is Rokhlin's original approach.

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