Work

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

Year: 2025

Type: article

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 .

Source: Revista Matemática Iberoamericana

DOI: 10.4171/rmi/1567

Authors: André Belotto da Silva, Adam Parusiński, Ludovic Rifford

Institutions: Institut Universitaire de France, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Université Côte d'Azur

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funder: Agence Nationale de la Recherche

Awards: Tropical aspects of singularities, Université de Paris