  We compute the fundamental group of each connected component of the space of
formal Legendrian embeddings in R3. We use it to show that previous examples in
the literature of non trivial loops of Legendrian embeddings are already non
trivial at the formal level. Likewise, we compute the fundamental group of the
different connected components of the space of formal horizontal embeddings
into the standard Engel R4. We check that this computes the fundamental group
of the space of horizontal embeddings as well.
