当前位置: X-MOL 学术J. Topol. Anal. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Expanders and right-angled Artin groups
Journal of Topology and Analysis ( IF 0.8 ) Pub Date : 2021-11-13 , DOI: 10.1142/s179352532150059x
Ramón Flores 1 , Delaram Kahrobaei 2, 3, 4, 5 , Thomas Koberda 6
Affiliation  

The purpose of this paper is to give a characterization of families of expander graphs via right-angled Artin groups. We prove that a sequence of simplicial graphs {Γi}i forms a family of expander graphs if and only if a certain natural mini-max invariant arising from the cup product in the cohomology rings of the groups {A(Γi)}i agrees with the Cheeger constant of the sequence of graphs, thus allowing us to characterize expander graphs via cohomology. This result is proved in the more general framework of vector space expanders, a novel structure consisting of sequences of vector spaces equipped with vector-space-valued bilinear pairings which satisfy a certain mini-max condition. These objects can be considered to be analogues of expander graphs in the realm of linear algebra, with a dictionary being given by the cup product in cohomology, and in this context represent a different approach to expanders that those developed by Lubotzky–Zelmanov and Bourgain–Yehudayoff.

中文翻译:

扩展器和直角 Artin 组

本文的目的是通过直角 Artin 群来描述扩展图族的特征。我们证明了一系列单纯图{Γ一世}一世当且仅当从组的上同调环中的杯积产生某个自然极小极大不变量时,才形成扩展图族{一种(Γ一世)}一世与图序列的 Cheeger 常数一致,因此允许我们通过上同调来表征扩展图。这个结果在更一般的框架下得到证明向量空间扩展器,一种新颖的结构,由向量空间序列组成,这些向量空间配备了满足某个最小最大条件的向量空间值双线性对。这些对象可以被认为是线性代数领域中扩展图的类似物,字典由上同调中的杯积给出,在这种情况下,代表了 Lubotzky-Zelmanov 和 Bourgain 开发的扩展器的不同方法-耶胡达奥夫。
更新日期:2021-11-13
down
wechat
bug