Infinitesimally polar Killing foliations via geometric resolutions

Abstract

We establish the strong Molino conjecture for complete infinitesimally polar singular Riemannian foliations and identify their Molino sheaves with those of their geometric resolutions. The resolution preserves basic and equivariant basic cohomology and transverse curvature bounds. These comparisons yield orbifold models and approximations of leaf-closure spaces, Euler localization, closed-leaf existence and Euler positivity under positive curvature, and transverse sphere theorems. Maximal defect gives a closed-ball leaf-closure space. Further applications include fundamental-group growth bounds and closedness under nonpositive transverse Ricci curvature that is negative definite at one regular point.