关于CAT（0）群边界的等变同胚
On equivariant homeomorphisms of boundaries of CAT(0) groups
摘要：
本文研究了CAT（0）群$G$几何作用于其上的两个真CAT（0）空间$X$和$Y$的边界$\partial X$和$\partial Y$的等变同胚.我们给出了一个充分条件，使两个边界$\partial X$和$\partial Y$的$G$ -等变同胚成为由$ϕ(gx_0)=gy_0$定义的拟等距$ϕ:Gx_0\to Gy_0$的连续扩张，其中$x_0\in X$和$y_0\in Y$ .
英文摘要：
In this paper, we investigate an equivariant homeomorphism of the boundaries $\partial X$ and $\partial Y$ of two proper CAT(0) spaces $X$ and $Y$ on which a CAT(0) group $G$ acts geometrically. We provide a sufficient condition to obtain a $G$-equivariant homeomorphism of the two boundaries $\partial X$ and $\partial Y$ as a continuous extension of the quasi-isometry $ϕ:Gx_0\to Gy_0$ defined by $ϕ(gx_0)=gy_0$, where $x_0\in X$ and $y_0\in Y$.
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