Global linearizable actions on topological manifolds

Tsemo Aristide; Yaounde Cameroon

paper

Global linearizable actions on topological manifolds

arXiv:2205.09417

Abstract

Let $M$ be a finite dimensional topological aspherical manifold whose universal cover is $R^{n}$ . In this paper, we study $A f f (M)$ , the subgroup of the group of homeomorphisms of $M$ , whose elements can be lifted to affine transformations of $R^{n}$ . We show that if $M$ is closed, the connected component $A f f (M)_{0}$ of $A f f (M)$ acts locally freely on $M$ . We deduce that $A f f (M)_{0}$ is a solvable Lie group, and is nilpotent if $M$ is a polynomial manifold. We study the foliation defined by the orbits of $A f f (M)_{0}$ if $d im (A f f (M)_{0}) = d im (M) - 1$ .

10 pages, 10 references