On equivariant homeomorphisms of boundaries of CAT(0) groups

Details On equivariant homeomorphisms of boundaries of CAT(0) groups On equivariant homeomorphisms of boundaries of CAT(0) groups

2010-04-25

arxiv.org/abs/1004.4376v4

Mathematics

Geometric Topology

15 pages

Scientific paper

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 $\phi:Gx_0\to Gy_0$ defined by $\phi(gx_0)=gy_0$, where $x_0\in X$ and $y_0\in Y$.

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