Reflection trees of graphs as boundaries of Coxeter groups

被引:1
|
作者
Swiatkowski, Jacek [1 ]
机构
[1] Uniwersytet Wroclawski, Inst Matematy, Wroclaw, Poland
来源
ALGEBRAIC AND GEOMETRIC TOPOLOGY | 2021年 / 21卷 / 01期
关键词
METRIC COMPACTA; MANIFOLDS;
D O I
10.2140/agt.2021.21.351
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
To any finite graph X (viewed as a topological space) we associate an explicit compact metric space X-r (X), which we call the reflection tree of graphs X. This space is of topological dimension <= 1 and its connected components are locally connected. We show that if X is appropriately triangulated (as a simplicial graph Gamma for which X is the geometric realization) then the visual boundary partial derivative(infinity) (W, S) of the right-angled Coxeter system (W, S) with the nerve isomorphic to Gamma is homeomorphic to X-r (X). For each X, this yields in particular many word hyperbolic groups with Gromov boundary homeomorphic to the space X-r (X).
引用
收藏
页码:351 / 420
页数:70
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