CAT(0) groups and Coxeter groups whose boundaries are scrambled sets
| dc.creator | Hosaka, Tetsuya | |
| dc.date | 2008-02-04 | |
| dc.date.accessioned | 2026-07-07T09:18:35Z | |
| dc.date.available | 2026-07-07T09:18:35Z | |
| dc.description | In this paper, we study CAT(0) groups and Coxeter groups whose boundaries are scrambled sets. Suppose that a group $G$ acts geometrically (i.e. properly and cocompactly by isometries) on a CAT(0) space $X$. (Such group $G$ is called a {\it CAT(0) group}.) Then the group $G$ acts by homeomorphisms on the boundary $\partial X$ of $X$ and we can define a metric $d_{\partial X}$ on the boundary $\partial X$. The boundary $\partial X$ is called a {\it scrambled set} if for any $α,β\in\partial X$ with $α\neqβ$, (1) $\limsup\{d_{\partial X}(gα,gβ) | g\in G\}>0$ and (2) $\liminf\{d_{\partial X}(gα,gβ) | g\in G\}=0$. We investigate when are boundaries of CAT(0) groups (and Coxeter groups) scrambled sets. | |
| dc.description | 28 pages | |
| dc.identifier | https://arxiv.org/abs/0802.0405 | |
| dc.identifier | http://arxiv.org/abs/0802.0405 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154076 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M07 | |
| dc.title | CAT(0) groups and Coxeter groups whose boundaries are scrambled sets | |
| dc.type | text |