A-foliations of codimension two on compact simply-connected manifolds

Abstract

We show that a singular Riemannian foliation of codimension two on a compact simply-connected Riemannian (n+2)-manifold, with regular leaves homeomorphic to the n-torus, is given by a smooth effective n-torus action. This solves in the negative for the codimension 2 case a question about the existence of foliations by exotic tori on simply-connected manifolds.