Acylindrical hyperbolicity of Artin-Tits groups associated to triangle-free graphs and cones over square-free bipartite graphs
Acylindrical hyperbolicity of Artin-Tits groups associated to triangle-free graphs and cones over square-free bipartite graphs
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与无三角形图和无正方形二分图上的锥体相关的 Artin-Tits 群的圆柱双曲性
DOI：
10.1017/s0017089520000555
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发表时间：
2020
影响因子：
0.5
通讯作者：
Shin-ichi Oguni
中科院分区：
文献类型：
--
作者：
Motoko Kato;Shin-ichi Oguni
据推测，任何不可约 Artin-Tits 群的中心商要么实际上是循环的，要么是圆柱双曲线的。我们根据 Brady 和 McCammond 的结果证明了 Artin-Tits 群的猜想，这些群被称为 CAT(0) 群，即与没有 3 圈的图相关的 Artin-Tits 群和与允许适当方向的图相关的几乎大类型的 Artin-Tits 群。特别是，后一个家族包含与无正方形二分图上的锥体相关的大型 Artin-Tits 群。
It is conjectured that the central quotient of any irreducible Artin–Tits group is either virtually cyclic or acylindrically hyperbolic. We prove this conjecture for Artin–Tits groups that are known to be CAT(0) groups by a result of Brady and McCammond, that is, Artin–Tits groups associated with graphs having no 3-cycles and Artin–Tits groups of almost large type associated with graphs admitting appropriate directions. In particular, the latter family contains Artin–Tits groups of large type associated with cones over square-free bipartite graphs.