On locally trivial extensions of topological spaces by a pseudogroup
In this paper we restrict ourselves to the particular case where the pseudogroup is $Γ\ltimes G$ given by the action of a dense subgroup $Γ$ of a Lie group $G$ acting on $G$ by left translations. For a Riemannian foliation $F$ on a complete Riemannian manifold $M$ which is transversally parallelizable in the sense of Molino, let $X$ be the space of leaves closures. The holonomy pseudogroup of $F$ is an example of a locally trivial extension of $X$ by $Γ\ltimes G$. The study of a generalization of this particular case shall be the main purpose of this paper.
math.AT↗