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The purpose of these notes is to explain parts of Gromov's survey ofCarnot-Carathedory spaces, in the light of subsequent results of M. Rumin.Among the rich material provided by Gromov, most of which pertains to analysison metric spaces, we choose to concentrate on the H{\"o}lder equivalenceproblem for Carnot manifolds. The notes go to some extent into the PDEtechnique used by Gromov in order to construct horizontal submanifolds. Rumin'scomplex is explained too. The upshot is that both methods yield more or lessthe same conclusions as far as the H{\"o}lder equivalence problem is concerned.

Submanifolds and differential forms on Carnot manifolds, after M. Gromov and M. Rumin