# A-Foliations of codimension two on compact simply-connected manifolds

## TL;DR

This paper proves that singular Riemannian foliations of codimension two with regular leaves homeomorphic to tori on compact simply-connected manifolds are induced by smooth torus actions, resolving a question about exotic tori.

## Contribution

It establishes that such foliations are always generated by smooth torus actions, providing a classification result for these geometric structures.

## Key findings

- Foliations with regular leaves homeomorphic to tori are given by smooth torus actions.
- The result negatively answers the existence of exotic tori foliations on simply-connected manifolds.
- The paper classifies singular Riemannian foliations of codimension two in this setting.

## 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.