Abnormal Singular Foliations and the Sard Conjecture for generic co-rank one distributions
Differential Geometry
2025-06-09 v2
Abstract
Given a smooth totally nonholonomic distribution on a smooth manifold, we construct a singular distribution capturing essential abnormal lifts which is locally generated by vector fields with controlled divergence. Then, as an application, we prove the Sard Conjecture for rank 3 distribution in dimension 4 and generic distributions of corank 1.
Cite
@article{arxiv.2310.20284,
title = {Abnormal Singular Foliations and the Sard Conjecture for generic co-rank one distributions},
author = {A Belotto da Silva and A Parusiński and L Rifford},
journal= {arXiv preprint arXiv:2310.20284},
year = {2025}
}