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Abstract: In this paper, we investigate an equivariant homeomorphism of the boundaries$\partial X$ and $\partial Y$ of two proper CAT0 spaces $X$ and $Y$ on whicha CAT0 group $G$ acts geometrically. We provide a sufficient condition toobtain a $G$-equivariant homeomorphism of the two boundaries $\partial X$ and$\partial Y$ as a continuous extension of the quasi-isometry $\phi:Gx 0\toGy 0$ defined by $\phigx 0=gy 0$, where $x 0\in X$ and $y 0\in Y$.



Author: Tetsuya Hosaka

Source: https://arxiv.org/



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