Riemannian foliations on simply connected manifolds and actions of tori on orbifolds (Q914163)

A relationship between Riemannian foliations and actions of tori is established: Theorem. If \({\mathcal F}\) is a Riemannian foliation of a compact simply connected manifold Y, then there exist a unique up to isomorphism effective smooth action of a torus \(T^ n\) on a simply connected compact orbifold X and a dense contractible subgroup L of \(T^ n\) such that the holonomy pseudogroups of \({\mathcal F}\) and of the foliation of X by the orbits of L are equivalent.