Rokhlin's Theorem (Intersection Forms)

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This proof is about Rokhlin's Theorem in the context of intersection forms. For other uses, see Rokhlin's Theorem.

Theorem

Let $M$ be a smooth 4-manifold.

Then:

$\map {\omega_2} {\map T M} = 0 \implies \operatorname {sign} Q_M = 0 \pmod {16}$

where:

$Q_M$ is the intersection form
$\map T M$ is the tangent bundle
$\omega_2$ is the second Stiefel-Whitney class.


Proof






Source of Name

This entry was named for Vladimir Abramovich Rokhlin.