We compute the fundamental group of each connected component of the space of formal Legendrian
embeddings in
.
We use it to show that previous examples in the literature of nontrivial
loops of Legendrian embeddings are already nontrivial 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
.
We check that the natural inclusion of the space of horizontal embeddings
into the space of formal horizontal embeddings induces an isomorphism at
–level.
Departamento de Álgebra, Geometría y
Topología, Facultad de Matemáticas, Universidad Complutense de
Madrid, and Instituto de Ciencias Matemáticas
CSIC-UAM-UC3M-UCM
Madrid
Spain
Departamento de Álgebra, Geometría y
Topología, Facultad de Matemáticas, Universidad Complutense de
Madrid, and Instituto de Ciencias Matemáticas
CSIC-UAM-UC3M-UCM
Madrid
Spain
