We bound the nuclear dimension of crossed products associated to some partial actions of finite groups or $\mathbb{Z}$ on finite dimensional locally compact Hausdorff second countable spaces. Our results apply to globalizable partial actions, finite group partial actions, minimal partial automorphisms, and partial automorphisms acting on zero-dimensional spaces, or a class of one dimensional spaces, containing 1-dimensional CW complexes. This extends work on global systems by Hirshberg and Wu.

中文翻译：

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与部分动力系统相关的交叉产品的核尺寸

我们限制了与有限群的某些部分作用或 $\mathbb{ž}$在有限维局部紧Hausdorff第二可数空间上。我们的结果适用于在零维空间或一维空间中包含一维CW复合体的可全局化局部动作，有限组局部动作，最小局部自同构和局部自同构。这扩展了Hirshberg和Wu在全球系统上的工作。