论文标题
亚组和过滤末端的准等级刚度刚度
Quasi-isometric rigidity of subgroups and Filtered ends
论文作者
论文摘要
令$ g $和$ h $为准时生成的组，让$ p \ leq g $;是否存在$ h $的亚组$ q $（或亚组集合），其左cosets的左cosets的左cosets的几何形状在$ g $中反映出左上方的几何形状？我们探索足够的条件以获得积极的答案。 本文考虑了$（g，\ natercal {p}）$的形式对，其中$ g $是有限生成的组，$ \ mathcal {p} $是一个有限的子组集合，有一个准静态的概念，对，以及准语言上的特征性特征性的子组集合。如果亚组属于质量特征，则是质量组。我们在文献中已经研究了有关准杂志刚度的文献中的不同类别的质量特征集，我们在其中一些文章中列出了其中一些并提供了其他示例。 本文的第一部分证明了：如果$ g $和$ h $是有限生成的准等级组，而$ \ nathcal {p} $是$ g $的子组的质量收集，那么子组有一组子组$ \ \ \ m nathcal {q} $ h $ $ h $ $ h $（$ h $ h $（$ h $） \ Mathcal {Q}）$是准递归对。 本文的第二部分研究了一对一组的过滤终点的$ \ tilde e（g，p）$，这是鲍迪奇介绍的一个概念，并提供了我们的主要结果的应用：如果$ g $和$ h $是Quasi ismemoptric群体和$ p \ leq g $ g $ g $是qu-characterstic，那就是$ q \ le q \ leq leq eq h $ ex exe = e（e） （H，Q）$。
Let $G$ and $H$ be quasi-isometric finitely generated groups and let $P\leq G$; is there a subgroup $Q$ (or a collection of subgroups) of $H$ whose left cosets coarsely reflect the geometry of the left cosets of $P$ in $G$? We explore sufficient conditions for a positive answer. The article consider pairs of the form $(G,\mathcal{P})$ where $G$ is a finitely generated group and $\mathcal{P}$ a finite collection of subgroups, there is a notion of quasi-isometry of pairs, and quasi-isometrically characteristic collection of subgroups. A subgroup is qi-characteristic if it belongs to a qi-characteristic collection. Distinct classes of qi-characteristic collections of subgroups have been studied in the literature on quasi-isometric rigidity, we list in the article some of them and provide other examples. The first part of the article proves: if $G$ and $H$ are finitely generated quasi-isometric groups and $\mathcal{P}$ is a qi-characteristic collection of subgroups of $G$, then there is a collection of subgroups $\mathcal{Q}$ of $H$ such that $ (G, \mathcal{P})$ and $(H, \mathcal{Q})$ are quasi-isometric pairs. The second part of the article studies the number of filtered ends $\tilde e (G, P)$ of a pair of groups, a notion introduced by Bowditch, and provides an application of our main result: if $G$ and $H$ are quasi-isometric groups and $P\leq G$ is qi-characterstic, then there is $Q\leq H$ such that $\tilde e (G, P) = \tilde e (H, Q)$.
