Characterizing a vertex‐transitive graph by a large ball
Characterizing a vertex‐transitive graph by a large ball
复制标题
用大球表征顶点传递图
作者：
Mikael de la Salle;R. Tessera
众所周知，完备黎曼流形M如果局部等距于对称空间，则它被对称空间覆盖。在这里，我们证明了这个性质的离散版本（称为局部到全局刚性）适用于一大类顶点传递图，包括简单李群中无挠格的Cayley图和无挠虚幂零群的Cayley图。相比之下，我们展示了各种例子的凯莱图的非线性提出的群体（例如，SL 4（Z））没有这个属性，回答了一个问题的Benjamini和Georgakopoulos。
It is well known that a complete Riemannian manifold M which is locally isometric to a symmetric space is covered by a symmetric space. Here, we prove that a discrete version of this property (called local to global rigidity) holds for a large class of vertex‐transitive graphs, including Cayley graphs of torsion‐free lattices in simple Lie groups, and Cayley graphs of torsion‐free virtually nilpotent groups. By contrast, we exhibit various examples of Cayley graphs of finitely presented groups (for example, SL4(Z) ) which fail to have this property, answering a question of Benjamini and Georgakopoulos.
影响因子：
1
作者：
Georgakopoulos A
通讯作者：
Georgakopoulos A