Quasi-isometry classification of right-angled Artin groups that split over cyclic subgroups
Quasi-isometry classification of right-angled Artin groups that split over cyclic subgroups
复制标题
在循环子群上分裂的直角 Artin 群的拟等距分类
DOI：
10.4171/ggd/584
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Alexander Margolis
中科院分区：
文献类型：
--
作者：
Alexander Margolis
对于单端直角 Artin 群，我们根据其定义图给出了无限循环子群上的 JSJ 圆柱树的显式描述。然后用它来将某些直角 Artin 群分类为准等距。特别是，我们证明如果两个直角 Artin 群是准等距的，那么它们的 JSJ 圆柱树是弱等价的。与此相反的情况则不一定成立。然而，对于一大类直角 Artin 群，我们可以定义称为拉伸因子的准等距不变量。然后我们证明，当且仅当两个这样的直角 Artin 群的 JSJ 圆柱体弱等价且具有匹配的拉伸因子时，它们才是准等距的。
For a one-ended right-angled Artin group, we give an explicit description of its JSJ tree of cylinders over infinite cyclic subgroups in terms of its defining graph. This is then used to classify certain right-angled Artin groups up to quasi-isometry. In particular, we show that if two right-angled Artin groups are quasi-isometric, then their JSJ tree of cylinders are weakly equivalent. The converse to this is not necessarily true. However, for a large class of right-angled Artin groups, one can define quasi-isometry invariants known as stretch factors. We then show that two such right-angled Artin groups are quasi-isometric if and only if their JSJ tree of cylinders are weakly equivalent and have matching stretch factors.
准等距群到直角 Artin 群
影响因子：
2.5
作者：
Huang, Jingyin;Kleiner, Bruce
通讯作者：
Kleiner, Bruce