连续传递循环群的分类

局部紧收敛群与n-传递作用

Locally compact convergence groups and n-transitive actions

除了n= 2，3当M是无限的不连通的时，所有的σ紧的，局部紧群都是n-传递连续作用在紧空间M上的.我们表明，没有这样的行动存在n=2和这些行动n=3的行动相吻合的双曲群的空间等变同胚的双曲边界。进一步给出了在无限紧集上3-适当传递作用的非紧群为非初等边界传递双曲群的一个刻划。主要工具是一个推广到局部紧群的鲍迪奇的拓扑特征的双曲群。最后，与n=3的情形相反，我们证明了当n>3时，如果一个局部紧群连续地、n-真地、n-余紧地作用在一个局部连通可度量化紧上，则M有一个局部割点.

关于大直径有限点传递图的标度极限

On the scaling limit of finite vertex transitive graphs with large diameter

设$(X_n)$是一个无界的有限连通点可迁图序列，使得对于某些$q>0$，有$ |X_n | = o(diam(X_n)^q)$.我们表明，采取一个子序列，并重新缩放后的直径，序列$(X_n)$收敛在Gromov Hausdorff距离的尺寸$<q$环面，配备了一些不变的芬斯勒度量。证明依赖于最近的定量版本格罗莫夫定理的群体与多项式增长获得Breuillard，绿色和陶。如果$X_n$只是粗略地传递和$|X_n| = o\bigl({diam(X_n)^δ}\bigr)$的$δ> 1$足够小，我们证明，这一次的初等手段，即$(X_n)$收敛到一个圆。

Triple transitivity and non-free actions in dimension one

The transitivity degree of a group $G$ is the supremum of all integers $k$ such that $G$ admits a faithful $k$-transitive action. Few obstructions are known to impose an upper bound on the transitivity degree for infinite groups. The results of this article provide two new classes of groups whose transitivity degree can be computed, as a corollary of a classification of all $3$-transitive actions of these groups. More precisely, suppose that $G$ is a subgroup of the homeomorphism group of the circle $\mathsf{Homeo}(\mathbb{S}^1)$ or the automorphism group of a tree $\mathsf{Aut}(\mathbb{T})$. …

一个具有(T)性质、作用于圆周的群

A group with Property (T) acting on the circle

该研究构造了一个具有(T)性质、作用于圆周的不可数完全不连通闭拓扑群，证明其作用共轭唯一且不可光滑化，并确定了该群的泛极小流。

Random Schreier graphs and expanders

Let the group $G$ act transitively on the finite set $Ω$, and let $S \subseteq G$ be closed under taking inverses. The Schreier graph $Sch(G \circlearrowleft Ω,S)$ is the graph with vertex set $Ω$ and edge set $\{ (ω,ω^s) : ω\in Ω, s \in S \}$. In this paper, we show that random Schreier graphs on $C \log|Ω|$ elements exhibit a (two-sided) spectral gap with high probability, magnifying a well known theorem of Alon and Roichman for Cayley graphs. On the other hand, depending on the particular action of $G$ on $Ω$, we give a lower bound on the number of elements which are necessary to provide a …