AI 中文总结
本文引入碰撞秩概念，证明有限碰撞秩群在4-流形拓扑中是好的，并构造了碰撞秩为二的有限生成群，其例子来自Sturmian系统拓扑全群的换位子群，包含连续统多个两两不同构的无限简单可遗群。
AI 中文摘要
我们引入碰撞秩，并证明有限碰撞秩的群在拓扑4-流形理论意义上是好的。我们证明了碰撞秩为二的有限生成群存在于次指数可遗群类之外。此类例子由Sturmian系统的拓扑全群的换位子群给出，并包含连续统多个两两不同构的无限简单可遗群。
英文摘要
We introduce collision rank and show that groups of finite collision rank are good in the sense of topological $4$-manifold theory. Finitely generated groups of collision rank two are shown to exist outside the class of subexponentially amenable groups. Such examples are given by commutator subgroups of topological full groups of Sturmian systems, and include continuum many pairwise nonisomorphic infinite simple amenable groups.
