Manifolds with aspherical singular Riemannian foliations

In the present work we study $A$-foliations, i.e. singular Riemannian foliations with regular leaf aspherical. The main result is that, for a simply-connected closed $(n+2)$-manifold $M$, an $A$-foliation with regular leaves of codimension $2$ in $M$ is homogeneous. In other words it is given by a smooth effective action of the torus $\mathbb{T }^n$ on $M$ by isometries.

We will give some conditions to compare two simply-connected, closed manifolds with $A$-foliations, up to foliated homeomorphism, via their leaf spaces.