论文标题
与两端边组的几乎免费组的图形图形的准静电刚度
Quasi-isometric rigidity for graphs of virtually free groups with two-ended edge groups
论文作者
论文摘要
我们研究了一个有限生成的基团的准时刚度刚度，这些基团分裂为具有几乎自由顶点组和两端边缘组的组的图表。让$ g $是一个相对于几乎是阿贝里亚亚组的单一，双曲线的组，并且在两端的子组上具有JSJ分解，该子组仅包含几乎没有四边形悬挂的几乎没有免费的顶点组。我们的主要结果是，任何$ g $的类准等级都可以抽象地符合$ g $。特别是，我们的结果适用于自由组对环状亚组的某些“通用” HNN扩展。
We study the quasi-isometric rigidity of a large family of finitely generated groups that split as graphs of groups with virtually free vertex groups and two-ended edge groups. Let $G$ be a group that is one-ended, hyperbolic relative to virtually abelian subgroups, and has JSJ decomposition over two-ended subgroups containing only virtually free vertex groups that aren't quadratically hanging. Our main result is that any group quasi-isometric to $G$ is abstractly commensurable to $G$. In particular, our result applies to certain "generic" HNN extensions of a free group over cyclic subgroups.
