2022/08/11 by Oleksandra Khokhliuk, Khokhliuk, Oleksandra, Sergiy Maksymenko +1 · 1 citation
Mathematics · #57R30 #57T20 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2208.05876
openalex publication_date 2022/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let F be a foliation with a "singular" submanifold B on a smooth manifold M and p:E → B be a regular neighborhood of B in M. Under certain "homogeneity" assumptions on F near B we prove that every leaf preserving diffeomorphism h of M is isotopic via a leaf preserving isotopy to a diffeomorphism which coincides with some vector bundle morphism of E near B. This result is mutually a foliated and compactly supported variant of a well known statement that every diffeomorphism h of ℝn fixing the origin is isotopic to the linear isomorphism induced by its Jacobi matrix of h at 0. We also present applications to the computations of the homotopy type of the group of leaf preserving diffeomorphisms of F.