2018/11/14 by Francisco-Javier Turiel, Antonio Viruel, Turiel, F. J. +1
Mathematics · #37C10 #37C85 #57S17 #Advanced Differential Equations and Dynamical Systems #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1811.05840
openalex publication_date 2018/11/14 · openalex created_date 2018/11/29 · openalex updated_date 2026/07/28
In a previous work it is shown that every finite group G of diffeomorphisms of a connected smooth manifold M of dimension ≥ 2 equals, up to quotient by the flow, the centralizer of the group of smooth automorphisms of a G-invariant complete vector field X (shortly X describes G). Here the foregoing result is extended to show that every finite group of diffeomorphisms of M is described, within the group of all homeomorphisms of M, by a vector field. As a consequence, it is proved that a finite group of homeomorphisms of a compact connected topological 4-manifold, whose action is free, is described by a continuous flow.