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.

35 pages, 3 figures. Proposition 4.3 is now Theorem B in the introduction and Proposition 3.3 in the text. Corollary 4.8 appears now also as Theorem D. We added a question in page 5 of the Introduction. Section 3 of the previous version is now Section 6. Section 3.1 is now Section 6.2 and Section 3.2 is now Section 6.1. Remark 4.9 has been added

References in corpus (2)

• Orbifolds from a metric viewpoint
• Riemannian foliation with exotic tori as leaves