Abnormal Singular Foliations and the Sard Conjecture for generic co-rank one distributions

2023/10/31 by da Silva, A Belotto, Parusiński, A, Rifford, L · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/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.

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