Geometric resolution of singular Riemannian foliations

Abstract

We prove that an isometric action of a Lie group on a Riemannian manifold admits a resolution preserving the transverse geometry if and only if the action is infinitesimally polar. We provide applications concerning topological simplicity of several classes of isometric actions, including polar and variationally complete ones. All results are proven in the more general case of singular Riemannian foliations.

Topological implications corrected and improved

References in corpus (1)

• Proofs of Conjectures about singular riemannian foliations

Cited by in corpus (1)

• Desingularization of singular Riemannian foliation