# 11. Distributions and the Frobenius Theorem

We define the notion of a *distribution* $ \Delta$ on a manifold $M$. We explain what is means for a distribution to be *integrable*, and prove the *Local Frobenius Theorem* which gives a necessary and sufficient condition for a distribution to be integrable.

We then define *foliations*** **and sketch a proof of the *Global Frobenius Theorem*, which states that a distribution is integrable if and only if it is induced by a foliation.

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