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Using a rigidity property of the foliations of $S^2 \times [0, 1]$ that aredefined by a non-vanishing closed one-form, we give a rather simple proof of atheorem due J. Cerf, going back to 1968, that the group of directdiffeomorphisms of $S^3$ is connected.

About the diffeomorphisms of the 3-sphere and a famous theorem of Cerf ($\Gamma_4 = 0$)