preprint
Inserted: 19 mar 2024
Last Updated: 19 mar 2024
Year: 2019
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.