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Abnormal singular foliations and the Sard conjecture for generic co-rank one distributions

  • André Belotto da Silva

    Institut de Mathématiques de Jussieu-Paris Rive Gauche, France; Institut universitaire de France (IUF), Paris, France
    ORCID

  • Adam Parusiński

    Université Côte d’Azur, Nice, France
    ORCID

  • Ludovic Rifford

    Université Côte d’Azur, Nice, France
    ORCID
Abnormal singular foliations and the Sard conjecture for generic co-rank one distributions cover

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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 distribution in dimension and generic distributions of corank .

Cite this article

André Belotto da Silva, Adam Parusiński, Ludovic Rifford, Abnormal singular foliations and the Sard conjecture for generic co-rank one distributions. Rev. Mat. Iberoam. (2025), published online first

DOI 10.4171/RMI/1567