Geometric resolution of singular Riemannian foliations

Alexander Lytchak

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arXiv · 0904.2019

Geometric resolution of singular Riemannian foliations

Alexander Lytchak

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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.

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Alexander Lytchak. 2010-02-16. Geometric resolution of singular Riemannian foliations. https://arxiv.org/abs/0904.2019

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