论文标题
在具有微支持动作的基团的稳定器上
On the stabilisers of points in groups with micro-supported actions
论文作者
论文摘要
给定首先要计算的Hausdorff Space $ \ Mathcal {X} $的同型同态的$ G $，我们证明，如果$ g $在$ \ mathcal {x} $上的动作是最小的$ \ MATHCAL {X} $。这使我们能够研究许多类别中的点的稳定器，例如拓扑完整的Cantor Minimal Systems，Thompson群体，分支组和作用于几乎规定的当地行动的树木的小组。
Given a group $G$ of homeomorphism of a first-countable Hausdorff space $\mathcal{X}$, we prove that if the action of $G$ on $\mathcal{X}$ is minimal and has rigid stabilisers that act locally minimally, then the neighbourhood stabilisers of any two points in $\mathcal{X}$ are conjugated by a homeomorphism of $\mathcal{X}$. This allows us to study stabilisers of points in many classes of groups, such as topological full groups of Cantor minimal systems, Thompson groups, branch groups, and groups acting on trees with almost prescribed local actions.
