几何特性 (T) 和卡兹丹投影

IF 0.8 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2024-07-01 DOI:10.1112/blms.13111

I. Vergara

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引用次数: 0

摘要

我们通过在最大均匀罗厄代数 C u , max ∗ ( X ) $C_{u,\max }^*(X)$ 中存在某种投影来描述几何性质 (T)，从而将群的卡兹丹投影概念扩展到公度空间领域。我们还用把度量空间分解成粗连接成分的方法来描述这种投影。

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Geometric property (T) and Kazhdan projections

We characterise Geometric Property (T) by the existence of a certain projection in the maximal uniform Roe algebra $C_{u, \max}^{*} (X)$ , extending the notion of Kazhdan projection for groups to the realm of metric spaces. We also describe this projection in terms of the decomposition of the metric space into coarsely connected components.