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 $y_0\in Y$.

15 pages

References in corpus (2)

• Rank one isometries of buildings and quasi-morphisms of Kac-Moody groups
• All CAT(0) Boundaries of a Group of the Form HxK are CE Equivalent

Cited by in corpus (1)

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