初等Amenable Groups盒空间的渐近维数
The Asymptotic Dimension of Box Spaces for Elementary Amenable Groups
摘要：
我们证明了盒空间的渐近维数关于群的扩张具有（次）可加性。结果得到，对于初等顺从群，它的任意盒空间的渐近维数都由它的Hirsch长度上界。这个绑定被证明是一个平等的一个大子类的群体，包括所有几乎多环的群体。
英文摘要：
We show that the asymptotic dimension of box spaces behaves (sub)additively with respect to extensions of groups. As a result, we obtain that for an elementary amenable group, the asymptotic dimension of any of its box spaces is bounded above by its Hirsch length. This bound is shown to be an equality for a large subclass of groups including all virtually polycyclic groups.
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