论文标题
完全断开局部紧凑的组的几何舒适性
Geometric amenability in totally disconnected locally compact groups
论文作者
论文摘要
我们给出了Soardi＆Woess and Salvatori结果的简短几何证据，即当且仅当其自动形态群是可以正常且单模型的时，准惯用图是可以正常的。我们还通过证明完全断开的本地紧凑型组可以在有界度的符合度的amenable图上进行适当的Lipschitz动作，从而增强了这一结果的一个方向，那么该组是可正常的且无象形的。我们通过局部紧凑型组的几何舒适性的概念，该群体先前已由第二作者研究，并通过类比定义了具有合理性的定义，仅使用正确的folner集代替左侧的folner集。我们还引入了局部紧凑型组的统一几何不典型性的概念，并以各种方式将该概念联系起来，以在图表上的作用及其模块化同态。
We give a short geometric proof of a result of Soardi & Woess and Salvatori that a quasitransitive graph is amenable if and only if its automorphism group is amenable and unimodular. We also strengthen one direction of that result by showing that if a compactly generated totally disconnected locally compact group admits a proper Lipschitz action on a bounded-degree amenable graph then that group is amenable and unimodular. We pass via the notion of geometric amenability of a locally compact group, which has previously been studied by the second author and is defined by analogy with amenability, only using right Folner sets instead of left Folner sets. We also introduce a notion of uniform geometric non-amenability of a locally compact group, and relate this notion in various ways to actions of that group on graphs and to its modular homomorphism.
