Abnormal Singular Foliations and the Sard Conjecture for generic co-rank one distributions
arXiv:2310.20284
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.