### Surface Foliation

Surface foliations are equivalent to holomorphic quadratic differentials on the surface.

Holomorphic 1-forms on a genus two surface. Each 1-form has two zeros, the space of all holomorphic 1-forms is 2g-2 dimensional.

Holomorphic quadratic differentials on a genus two surface. Each differential form has four zeros, the space of all holomorphic quadratic forms is 6g-6 dimensional.
If all the trajectories are finite, the differential is called a Strebel differential.

Holomorphic quadratic differentials on a genus two surface, the trajectories are inifinite.

Whitehead move.

Holomorphic quadratic differentials on a genus three surface.

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