Following Expose 6 of Thurston's Work on Surfaces, we will present the classification of measured foliations. Each measured foliation on a genus g > 1 surface can be put into a unique normal form up to isotopy. Such a normal form may be presented as the enlargement of a measured foliation on a disjoint union of annuli and pairs of pants contained in the manifold. One then easily deduces from this normal form that the space of projective measured foliations is a sphere of dimension 6g-7.
The Classification of Measured Foliations
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