Grigorchuk群的粗几何性质
oarse Geometric Properties of Grigorchuk group
本文主要介绍了Grigorchuk群的定义并研究了它的粗几何性质，在粗几何中，顺从性可以推出性质A和a-T-menable性质，而性质A和a-T-menable性质又可以推出粗嵌入到希尔伯特空间。主要利用Grigorchuk群的次指数增长性推出Grigorchuk群具有顺从性，并证明了Grigorchuk群的渐进维数为无限维。
In this paper,we introduce the definition of Grigorchuk group and study its coarse geometric properties. In Coarse geometry, amenable implies property A and a-T-menable, property A and a-T-menable implies coarse embedding into Hilbert space. we use the sub-exponential growth of Grigorchuk group to show that it is amenable,And the asymptotic dimension of Grigorchuk group is infinity.
王显金、秦一帆
数学
Grigorchuk群顺从性渐进维数
Grigorchuk groupamenableasymptotic dimension
王显金,秦一帆.Grigorchuk群的粗几何性质[EB/OL].(2022-02-25)[2025-08-24].http://www.paper.edu.cn/releasepaper/content/202202-75.点此复制
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