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

Abstract

AbstractWe show that a singular Riemannian foliation of codimension two on a compact simply-connected Riemannian $$(n+2)$$ ( 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.