Dynamic asymptotic dimension: relation to dynamics, topology, coarse geometry, and $$C^*$$ C ∗ -algebras
Dynamic asymptotic dimension: relation to dynamics, topology, coarse geometry, and $$C^*$$ C ∗ -algebras
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动态渐近维数：与动力学、拓扑、粗略几何和 $$C^*$$ C â -代数的关系
DOI：
10.1007/s00208-016-1395-0
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发表时间：
2017
影响因子：
1.4
通讯作者：
Yu, Guoliang
中科院分区：
文献类型：
--
作者：
Guentner, Erik;Willett, Rufus;Yu, Guoliang
我们引入动态渐近维数，一个概念的尺寸的作用的离散群的局部紧空间，更一般的局部紧的étale广群胚。我们研究我们的概念最小行动的整数组，它的关系与条件所使用的巴特尔斯，Lück，和赖希的背景下，控制拓扑结构，其连接与格罗莫夫的理论的渐近维数。我们还表明，动态渐近维数给出了边界的核尺寸的冬季和Zacharias为代数与动力系统。动力学渐近维数也对K-理论和流形拓扑学有影响：这些将在后续工作中得到阐述。
We introduce dynamic asymptotic dimension, a notion of dimension for actions of discrete groups on locally compact spaces, and more generally for locally compact étale groupoids. We study our notion for minimal actions of the integer group, its relation with conditions used by Bartels, Lück, and Reich in the context of controlled topology, and its connections with Gromov’s theory of asymptotic dimension. We also show that dynamic asymptotic dimension gives bounds on the nuclear dimension of Winter and Zacharias for-algebras associated to dynamical systems. Dynamic asymptotic dimension also has implications forK-theory and manifold topology: these will be drawn out in subsequent work.