论文标题
具有在圆圈上作用（t）的集团
A group with Property (T) acting on the circle
论文作者
论文摘要
我们展示了一个拓扑组$ g $，其财产（t）在圆圈上表现出非元素和连续的作用。该组是$ \ operatorname {holeo}^+（\ mathbf {s}^1）$的完全断开的封闭子组。它具有较大的统一双重，因为它可以分开点。它来自树突的同构和万花筒结构。或者，它可以看作是保留双曲盘的某些特定测量层压的元素。 我们还证明，这种动作是独一无二的结合，并且不能以任何方式平滑。最后，我们确定集团$ g $的通用最小流量。
We exhibit a topological group $G$ with property (T) acting non-elementarily and continuously on the circle. This group is an uncountable totally disconnected closed subgroup of $\operatorname{Homeo}^+(\mathbf{S}^1)$. It has a large unitary dual since it separates points. It comes from homeomorphisms of dendrites and a kaleidoscopic construction. Alternatively, it can be seen as the group of elements preserving some specific geodesic lamination of the hyperbolic disk. We also prove that this action is unique up to conjugation and that it can't be smoothened in any way. Finally, we determine the universal minimal flow of the group $G$.
