2022/05/19 by Aristide Tsemo, Aristide, Tsemo, Yaounde Cameroon +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2205.09417
openalex publication_date 2022/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a finite dimensional topological aspherical manifold whose universal cover is \bf Rn. In this paper, we study Aff(M), the subgroup of the group of homeomorphisms of M, whose elements can be lifted to affine transformations of \bf Rn. We show that if M is closed, the connected component Aff(M)0 of Aff(M) acts locally freely on M. We deduce that Aff(M)0 is a solvable Lie group, and is nilpotent if M is a polynomial manifold. We study the foliation defined by the orbits of Aff(M)0 if dim(Aff(M)0)=dim(M)-1.