粗糙顺应性与仿紧性
Coarse amenability versus paracompactness
摘要：
最近的研究在粗糙的几何揭示了某些概念之间的相似性分析，大规模几何和拓扑结构。G.Yu的性质A是群的顺从性的粗略模拟，它的推广（精确空间）后来被加强为使用单位分割的仿紧空间的大规模模拟。在这篇文章中，我们将更深入地揭示粗糙柔顺性和仿紧性之间的类比。特别是，我们定义了一个新的粗糙模拟仿紧建模的定义特征的扩展。这个类比给出了一个简单的证明，证明了三类空间是粗略不服从的：扩展序列，围长接近无穷大的图空间，以及有限非平凡群的幂的并集。
英文摘要：
Recent research in coarse geometry revealed similarities between certain concepts of analysis, large scale geometry, and topology. Property A of G.Yu is the coarse analog of amenability for groups and its generalization (exact spaces) was later strengthened to be the large scale analog of paracompact spaces using partitions of unity. In this paper we go deeper into divulging analogies between coarse amenability and paracompactness. In particular, we define a new coarse analog of paracompactness modelled on the defining characteristics of expanders. That analog gives an easy proof of three categories of spaces being coarsely non-amenable: expander sequences, graph spaces with girth approaching infinity, and unions of powers of a finite non-trivial group.
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