Dense subsets of boundaries of CAT(0) groups
| dc.creator | Hosaka, Tetsuya | |
| dc.date | 2005-10-24 | |
| dc.date.accessioned | 2026-07-07T06:47:51Z | |
| dc.date.available | 2026-07-07T06:47:51Z | |
| dc.description | In this paper, we study dense subsets of boundaries of CAT(0) groups. Suppose that a group $G$ acts geometrically on a CAT(0) space $X$ and suppose that there exists an element $g_0\in G$ such that (1) $Z_{g_0}$ is finite, (2) $X\setminus F_{g_0}$ is not connnected, and (3) each component of $X\setminus F_{g_0}$ is convex and not $g_0$-invariant, where $Z_{g_0}$ is the centralizer of $g_0$ and $F_{g_0}$ is the fixed-point set of $g_0$ in $X$ (that is, $Z_{g_0}=\{h\in G| g_0h=hg_0\}$ and $F_{g_0}=\{x\in X| g_0x=x\}$). Then we show that each orbit $G α$ is dense in the boundary $\partial X$ (i.e.\ $\partial X$ is minimal) and the set $\{g^{\infty} | g\in G, o(g)=\infty\}$ is also dense in the boundary $\partial X$. We obtain an application for dense subsets on the boundary of a Coxeter system. | |
| dc.identifier | https://arxiv.org/abs/math/0510511 | |
| dc.identifier | http://arxiv.org/abs/math/0510511 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103789 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M07 | |
| dc.title | Dense subsets of boundaries of CAT(0) groups | |
| dc.type | text |