标题： 循环序和Leary--Minasyan群在粗略$\mathrm{PD}(n)$空间上的作用 显示英文标题

标题： Cyclic orders and actions of Leary--Minasyan groups on coarse $\mathrm{PD}(n)$ spaces

摘要： 我们证明对于$n \geq 3$，存在挠率自由的 CAT(0) 群，其视觉边界可以嵌入到$S^n$中，但这些群并不是紧致的可缩 $n+1$-流形的基本群的有限指数子群。 这些群是之前由 Leary 和 Minasyan 构造的 CAT(0) 群，并且不是双自动群。 障碍来自于分析 Bass-Serre 树边界上的某些循环序，方式与 Kapovich-Kleiner 排除 Baumslag-Solitar 群在粗略的$\mathrm{PD}(3)$空间上的作用相同。 显示英文摘要

摘要： We show that for $n \geq 3$, there are torsion-free CAT(0) groups with visual boundaries that embed into $S^n$ but which are not virtually the fundamental group of a compact aspherical $n+1$-manifold. The groups are the CAT(0) and not bi-automatic groups constructed previously by Leary and Minasyan. The obstruction comes from analyzing certain cyclic orders on the boundary of the Bass-Serre tree, in the same manner as Kapovich-Kleiner ruled out actions of Baumslag-Solitar groups on coarse $\mathrm{PD}(3)$ spaces.