On equivariant homeomorphisms of boundaries of CAT(0) groups

Abstract

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 $\varphi :G{x}_0\to G{y}_0$ defined by $\varphi (g{x}_0)=g{y}_0$, where $x_0\in X$ and $y_0\in Y$.

arXiv comment15 pages

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Cited by in corpus (1)

• Cell-Like Equivalences and Boundaries of CAT(0) Groups