2017/03/21 by Sylvain Lavau, Lavau, Sylvain
Mathematics · Medicine · #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Spinal Hematomas and Complications
paper · pdf · doi:10.48550/arxiv.1703.07404
openalex publication_date 2017/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A singular (or Hermann) foliation on a smooth manifold M can be seen as a subsheaf of the sheaf \mathfrakX of vector fields on M. We show that if this singular foliation admits a resolution (in the sense of sheaves) consisting of sections of a graded vector bundle of finite type, then one can lift the Lie bracket of vector fields to a Lie ∞-algebroid structure on this resolution, that we call a universal Lie ∞-algebroid associated to the foliation. The name is justified because it is isomorphic (up to homotopy) to any other Lie ∞-algebroid structure built on any other resolution of the given singular foliation.