论文标题
通过真实线的同态近似近似非亚伯自由组
Approximating nonabelian free groups by groups of homeomorphisms of the real line
论文作者
论文摘要
We show that for a large class $\mathcal{C}$ of finitely generated groups of orientation preserving homeomorphisms of the real line, the following holds: Given a group $G$ of rank $k$ in $\mathcal{C}$, there is a sequence of $k$-markings $(G, S_n), n\in \mathbf{N}$ whose limit in the space of marked groups是带有标准标记的排名$ k $的免费组。我们认为的班级由接受满足轻度动态条件的行动和某些“自相似性”类型假设组成。例子包括汤普森（Thompson）的$ f $，希格曼·汤普森（Higman-Thompson）小组，斯坦 - 汤普森（Stein-Thompson）小组，各种比埃里·斯特雷贝尔（Bieri-Strebel）小组，黄金比率汤普森（Thompson Group），以及有限的一组分段投影型同构同构。对于汤普森（Thompson）的组$ f $，我们提供了一个新的，更简单的证明，证明了布林（Groups，Goem，几何和Dynamics 2010）证明了这一事实。
We show that for a large class $\mathcal{C}$ of finitely generated groups of orientation preserving homeomorphisms of the real line, the following holds: Given a group $G$ of rank $k$ in $\mathcal{C}$, there is a sequence of $k$-markings $(G, S_n), n\in \mathbf{N}$ whose limit in the space of marked groups is the free group of rank $k$ with the standard marking. The class we consider consists of groups that admit actions satisfying mild dynamical conditions and a certain "self-similarity" type hypothesis. Examples include Thompson's group $F$, Higman-Thompson groups, Stein-Thompson groups, various Bieri-Strebel groups, the golden ratio Thompson group, and finitely presented non amenable groups of piecewise projective homeomorphisms. For the case of Thompson's group $F$ we provide a new and considerably simpler proof of this fact proved by Brin (Groups, Geometry, and Dynamics 2010).
