Rokhlin's Theorem (Intersection Forms)


 * ''This article is on Rokhlin's Theorem for intersection forms. If your looking for Rokhlin's Theorem on zero-signature manifolds as boundaries, see this page.

Theorem
If $$M \ $$ is a smooth 4-manifold,

$$\omega_2(T(M))=0 \ \Longrightarrow \  \text{sign } Q_M=0 \text{ (mod 16)}$$

where $$Q_M \ $$ is the intersection form,$$T(M) \ $$ is the tangent bundle, and $$\omega_2$$ is the second Stiefel-Whitney class.