English

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.

Keywords

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}
}