Geometric resolution of singular Riemannian foliations

2009/04/13 by Alexander Lytchak, Lytchak, Alexander · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0904.2019

openalex publication_date 2009/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• On the Rational Hyperbolicity problem

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