The weak containment problem for étale groupoids which are strongly amenable at infinity

Non-amenable principal groupoids with weak containment

We construct examples of principal groupoids that have weak containment but are not amenable, thus answering questions by Claire Anantharaman-Delaroche and Rufus Willett.

étale群胚的下行原理与Baum-Connes猜想

A going-down principle for {é}tale groupoids and the Baum-Connes conjecture

本文扩展了étale群胚的下行原理，通过群胚单纯复形研究证明了一般étale群胚的Baum-Connes装配映射分裂单射，并应用于拓扑K-理论连续性和Künneth公式。

群胚的顺从性、精确性与弱包含性质

Amenability, exactness and weak containment property for groupoids

本文综述群胚$C^*$-代数的精确性概念，并探讨其在弱包含问题中的作用，即完全与约化$C^*$-代数一致是否蕴含群胚顺从性。

Some remarks about the weak containment property for groupoids and semigroups

A locally compact groupoid is said to have the weak containment property if its full $C^*$-algebra coincides with its reduced one. This property is strictly weaker than amenability and is known to be equivalent to amenability for transformation groupoids relative to actions of exact discrete groups. We believe that for general étale groupoids one should have the same equivalence of the two properties under some mild exactness assumption. In this paper we try to support this statement.

Roe代数和适用于étale群胚真作用的粗指标映射. I

Roe algebras and coarse index maps for spaces with proper actions of {é}tale groupoids. I

本文为étale群胚真作用空间建立等变Roe代数与K-理论框架，构造粗指标映射的接收函子，并证明满足条件的群胚单纯复形存在通用模。

étale群胚上Fell丛的C*-代数上的KMS态

KMS states on the $\mathrm{C}^*$-algebras of Fell bundles over {é}tale groupoids

本文证明了étale群胚上饱和Fell丛的全C*-代数上KMS态与迷向群上Fell丛C*-代数的可测态场之间的一一对应，建立了积分-分解定理，并通过群胚交叉积、矩阵代数等例子加以验证。