Artin-Tits B、A～和C～类型组的曲线图为双曲线

IF 1.1 Q1 MATHEMATICS

Transactions of the London Mathematical Society Pub Date : 2020-03-10 DOI:10.1112/tlm3.12029

M. Calvez, B. A. Cisneros de la Cruz

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引用次数: 5

摘要

不可约抛物子群的图是一个与Artin–Tits群a相关的组合对象，定义为当a是（n+1）链上的Artin编织群时，与（n+1）次穿刺盘的曲线图重合。在这种情况下，根据著名的马苏尔-明斯基定理，它是一个双曲图。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开放问题。在本文中，我们给出了部分肯定的答案。

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Curve graphs for Artin–Tits groups of type B , A∼ and C∼ are hyperbolic

The graph of irreducible parabolic subgroups is a combinatorial object associated to an Artin–Tits group A defined so as to coincide with the curve graph of the (n+1) ‐times punctured disk when A is Artin's braid group on (n+1) strands. 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.

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来源期刊

Transactions of the London Mathematical Society MATHEMATICS-

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

41 weeks