论文标题
全球可线化的动作对拓扑流形
Global linearizable actions on topological manifolds
论文作者
论文摘要
令$ m $为有限的尺寸拓扑非球面歧管，其通用封面为$ {\ bf r}^n $。 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 ${\bf R}^n$.我们表明，如果$ m $关闭，则连接的组件$ aff（m）_0 $ aff（m）$在$ m $上自由自由地行为。我们推断出$ aff（m）_0 $是一个可解决的谎言组，如果$ m $是多项式歧管，则nilpotent。 We study the foliation defined by the orbits of $Aff(M)_0$ if $dim(Aff(M)_0)=dim(M)-1$.
Let $M$ be a finite dimensional topological aspherical manifold whose universal cover is ${\bf R}^n$. 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 ${\bf R}^n$. 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 $dim(Aff(M)_0)=dim(M)-1$.
