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

2019/03/17 by Corro, Diego
#53C12 #53C24 #57R30 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.07191

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.

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