论文标题
用于动态渐近维度的Hurewicz型定理，应用于粗糙的几何和动力学
A Hurewicz-type Theorem for the Dynamic Asymptotic Dimension with Applications to Coarse Geometry and Dynamics
论文作者
论文摘要
我们证明了最初由Guentner，Willett和Yu引入的动态渐近维度的Hurewicz型定理。已知该维度的计算（或简单的上限）具有与小组作用的共同体及其转换组C*-Algebras的K理论有关的含义。此外，这些含义与C*-Algebras的当前分类程序有关。作为我们主要定理的必然性，我们显示了组对正常亚组沿顺序过滤沿顺序过滤的动作的动态渐近维度是对组的扩展的亚辅助性，这表明基础可融合的基团的许多这样的动作都是有限的。我们将其与其他新型结果相结合，将这种作用的动态渐近维度与相应盒子空间的渐近维度相结合。这使我们能够使用基本可育组的赫尔希长度的概括来对许多盒子空间的渐近维度（包括来自无数级生长的无限群体的示例）进行上限。对于其中一些示例，我们还可以通过利用群体的末端理论来找到下限。
We prove a Hurewicz-type theorem for the dynamic asymptotic dimension originally introduced by Guentner, Willett, and Yu. Calculations of (or simply upper bounds on) this dimension are known to have implications related to cohomology of group actions and the K-theory of their transformation group C*-algebras. Moreover, these implications are relevant to the current classification program for C*-algebras. As a corollary of our main theorem, we show the dynamic asymptotic dimension of actions by groups on profinite completions along sequential filtrations by normal subgroups is subadditive over extensions of groups, which shows that many such actions by elementary amenable groups are finite dimensional. We combine this with other novel results relating the dynamic asymptotic dimension of such an action to the asymptotic dimension of a corresponding box space. This allows us to give upper bounds on the asymptotic dimension of many box spaces (including examples from infinitely-many groups with exponential growth) using a generalization of the Hirsch length for elementary amenable groups. For some of these examples, we can also find lower bounds by utilizing the theory of ends of groups.
