Rokhlin's Theorem (Intersection Forms)

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.