On the dynamic asymptotic dimension of étale groupoids

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-26 DOI:10.1007/s00209-024-03492-x

Christian Bönicke

引用次数: 0

Abstract

We investigate the dynamic asymptotic dimension for étale groupoids introduced by Guentner, Willett and Yu. In particular, we establish several permanence properties, including estimates for products and unions of groupoids. We also establish invariance of the dynamic asymptotic dimension under Morita equivalence. In the second part of the article, we consider a canonical coarse structure on an étale groupoid, and compare the asymptotic dimension of the resulting coarse space with the dynamic asymptotic dimension of the underlying groupoid.

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论埃塔莱群集的动态渐近维度

我们研究了由 Guentner、Willett 和 Yu 引入的 étale 子群的动态渐近维度。特别是，我们建立了几个永恒性质，包括对群集的乘积和联合的估计。我们还建立了动态渐近维度在莫里塔等价性下的不变性。在文章的第二部分，我们考虑了一个 étale 类群上的典型粗糙结构，并比较了所得到的粗糙空间的渐近维度与底层类群的动态渐近维度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.