Curve graphs for Artin-Tits groups of type B, A~ and C~ are hyperbolic
Curve graphs for Artin-Tits groups of type B, A~ and C~ are hyperbolic
复制标题
B、A~ 和 C~ 型 Artin-Tits 群的曲线图是双曲的
DOI：
10.1112/tlm3.12029
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发表时间：
2021
影响因子：
0.8
通讯作者：
Calvez M
中科院分区：
文献类型：
--
作者：
Calvez M
不可约抛物子群的图是一个与Artin-Tits群相关联的组合对象，当Artin的辫子群在链上时，定义该组合对象与-次穿孔圆盘的曲线图重合。在这种情况下，它是一个双曲图，由著名的马苏尔-明斯基定理。更一般的Artin-Tits群的不可约抛物子群图的双曲性是一个重要的公开问题。本文给出了一个部分肯定的回答，证明了与球面型Artin-Tits群相关联的不可约抛物子群的图也同构于-次穿孔圆盘的曲线图;因此，它是双曲线的，因为，我们证明了与Artin-1相关的不可约抛物子群的图，欧几里得型和的山雀群与次穿孔圆盘的曲线图的某些非准等距嵌入的子图同构。尽管如此，我们证明，这些图是双曲的。
Thegraph of irreducible parabolic subgroupsis a combinatorial object associated to an Artin–Tits groupdefined so as to coincide with the curve graph of the‐times punctured disk whenis Artin's braid group onstrands. In this case, it is a hyperbolic graph, by the celebrated Masur–Minsky's theorem. Hyperbolicity of the graph of irreducible parabolic subgroups for more general Artin–Tits groups is an important open question. In this paper, we give a partial affirmative answer.For, we show that the graph of irreducible parabolic subgroups associated to the Artin–Tits group of spherical typeis also isomorphic to the curve graph of the‐times punctured disk; hence, it is hyperbolic.For, we show that the graphs of irreducible parabolic subgroups associated to the Artin–Tits groups of euclidean typeandare isomorphic to some subgraphs of the curve graph of the‐times punctured disk which are not quasi‐isometrically embedded. We prove nonetheless that these graphs are hyperbolic.