Laura Ribeiro dos Santos

arXiv2026

Infinitesimally polar Killing foliations via geometric resolutions

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.

math.DG↗

arXiv2026

Blown-up singular Riemannian foliations

We investigate new properties and applications of the blow-up desingularization method in the context of singular Riemannian foliations. First, we relate the dynamics of such a foliation, which is governed by the so-called Molino sheaf, with that of its blow-up. In the particular case of singular Killing foliations, this leads to a strong constraint: when the Euler characteristic of the ambient manifold is non-vanishing and the singular strata are all odd-codimensional, the leaves of such foliations are all closed. Next, we show that the space of leaf closures of a singular Killing foliation is the Gromov--Hausdorff limit of a sequence of orbifolds, whose dimensions are the codimension of the foliation. Finally, we relate the basic cohomology of a singular Riemannian foliation with that of its blow-up, generalizing well-known, classical analogous results in algebraic and complex geometry.

math.DG↗