论文标题
封闭的近似亚组：紧凑，舒适性和近似晶格
Closed approximate subgroups: compactness, amenability and approximate lattices
论文作者
论文摘要
我们研究了局部紧凑型组的封闭近似亚组的性质，对于近似晶格，即离散且具有有限的共卷的近似近似亚组。 我们证明了Cartan的封闭式群定理的大概子组版本，并研究了一些应用。我们以Breuillard的精神（green--tao定理）为封闭的近似亚组提供了一个结构定理。然后，我们证明了有关近似晶格的两个结果：我们扩展到迈耶（Meyer）导致数学准晶体的结构定理；我们证明了有关谎言基团的自由基相交的结果，以及由于Auslander，Bieberbach和Mostow引起的定理的离散近似亚组。作为一个基本主题，我们利用源自Hrushovski的工作以及Breuillard，Green和Tao的概念概念的概念。我们展示了如何从良好模型中绘制有关给定近似子组的信息。
We investigate properties of closed approximate subgroups of locally compact groups, with a particular interest for approximate lattices i.e. those approximate subgroups that are discrete and have finite co-volume. We prove an approximate subgroup version of Cartan's closed-subgroup theorem and study some applications. We give a structure theorem for closed approximate subgroups of amenable groups in the spirit of the Breuillard--Green--Tao theorem. We then prove two results concerning approximate lattices: we extend to amenable groups a structure theorem for mathematical quasi-crystals due to Meyer; we prove results concerning intersections of radicals of Lie groups and discrete approximate subgroups generalising theorems due to Auslander, Bieberbach and Mostow. As an underlying theme, we exploit the notion of good models of approximate subgroups that stems from the work of Hrushovski, and Breuillard, Green and Tao. We show how one can draw information about a given approximate subgroup from a good model, when it exists.
