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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.
Related
- Hyperpolarity of polar foliations of codimension two
- Geometric index theorems for holomorphic foliations and curves
- Infinitesimally Euclidean metric surfaces
- Characterizing multigraded regularity and virtual resolutions on products of projective spaces
- Isolated symplectic singularities admitting symplectic resolutions
BibTeX
@misc{jr2026infinitesimally,
title = {{Infinitesimally polar Killing foliations via geometric resolutions}},
author = {Francisco C. Caramello Jr. and Laura Ribeiro dos Santos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25582},
eprint = {2610.25582},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25582},
}
RIS
TY - UNPB
TI - Infinitesimally polar Killing foliations via geometric resolutions
AU - Francisco C. Caramello Jr.
AU - Laura Ribeiro dos Santos
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25582
UR - https://arxiv.org/abs/2610.25582
AB - 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.
ER -