论文标题
Artin-tits类型$ B $，$ \ widetilde a $和$ \ widetilde c $的曲线图是夸张的
Curve graphs for Artin-Tits groups of type $B$, $\widetilde A$ and $\widetilde C$ are hyperbolic
论文作者
论文摘要
\ emph {不可减至的抛物线子组的图是与Artin-tits组$ a $相关的组合对象，以便与$（n+1）$ - times times dunctust disk的曲线图相吻合时，当$ a $ a $ a $ a $ a aintin是$（n+1）$ strands上的artin brove in artin的辫子组。在这种情况下，这是著名的Masur-Minsky定理的双曲线图。对于更一般的Artin-tits组的肥大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。 对于$ n \ geqslant 3 $，我们证明了与球形类型$ b_n $相关的不可减至的抛物线子组的图也对$（n+1）$ - 乘以圆盘的曲线图也是同构的，因此是多余的。 对于$ n \ geqslant 2 $，我们表明与欧几里得类型$ \ widetilde a_n $和$ \ widetilde c_n $相关的不可约抛物线子组的图是与$（n+2）$ - tirs time的某些子图相同的，这是$（n+2）n dimct的某些子图形，这是$ - dimct的某些子图形，这是对$ - time的某些子图。尽管如此，我们证明这些图是双曲线。
The \emph{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 for more general Artin-Tits groups is an important open question. In this paper, we give a partial affirmative answer. For $n\geqslant 3$, we prove that the graph of irreducible parabolic subgroups associated to the Artin-Tits group of spherical type $B_n$ is also isomorphic to the curve graph of the $(n+1)$-times punctured disk, hence it is hyperbolic. For $n\geqslant 2$, we show that the graphs of irreducible parabolic subgroups associated to the Artin-Tits groups of euclidean type $\widetilde A_n$ and $\widetilde C_n$ are isomorphic to some subgraphs of the curve graph of the $(n+2)$-times punctured disk which are not quasi-isometrically embedded. We prove nonetheless that these graphs are hyperbolic.
