Hyperbolic right-angled Coxeter groups with boundaries as a Sierpinski carpet and a Menger curve
Hyperbolic right-angled Coxeter groups with boundaries as a Sierpinski carpet and a Menger curve
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双曲直角 Coxeter 群，其边界为谢尔宾斯基地毯和门格尔曲线
DOI：
10.1016/j.topol.2019.03.024
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发表时间：
2019
影响因子：
0.6
通讯作者：
Naotsugu Chinen; Tetsuya Hosaka
中科院分区：
文献类型：
--
作者：
坂内 真三;Naotsugu Chinen; Tetsuya Hosaka
设(W,S)为双曲直角Coxeter系统，其神经为一维强共通单纯复形，本文定义了“强共通”。然后我们提供 Coxeter 群 W 的表征，其边界 ∂ W 是 Sierpiński 地毯和门格尔曲线。利用这个结果，我们构造了以边界作为通用曲线的双曲直角 Coxeter 群。我们注意到，N. Benakli 的博士论文 [3] 中构建了以边界作为通用曲线的双曲非直角 Coxeter 群。
Let (W, S) be a hyperbolic right-angled Coxeter system whose nerve is a 1-dimensional strongly co-connected simplicial complex, where “strongly co-connected” is defined in this paper. Then we provide characterizations of the Coxeter group W whose boundary∂ W is a Sierpiński carpet and a Menger curve. Using this result, we construct hyperbolic right-angled Coxeter groups with boundaries as their universal curves. We note that hyperbolic non-right-angled Coxeter groups with boundaries as their universal curves have been constructed in N. Benakli's PhD Thesis [3].