论文标题
摩尔斯摩尔斯的规律性和稳定亚组的增长
Regularity of Morse geodesics and growth of stable subgroups
论文作者
论文摘要
我们证明，莫尔斯局部到全球群体的生长速度比其无限指数稳定亚组快。这概括了达哈曼尼（Dahmani），未来和明智的结果，在夸张组的准凸子群亚组的背景下，包含映射类组，CAT（0）组和封闭3个manifolds的基本组的广泛组。为了实现这一目标，我们在莫尔斯局部到全球群体中开发了一种自动结构理论。这些自动结构的其他应用包括在普通语言，稳定亚组生长的合理性方面对稳定子组的描述，摩尔斯元素吸引固定点的密度以及在任何无限正常亚组的极限集中的摩尔斯元素的固定点的密度。
We prove that Morse local-to-global groups grow exponentially faster than their infinite index stable subgroups. This generalizes a result of Dahmani, Futer, and Wise in the context of quasi-convex subgroups of hyperbolic groups to a broad class of groups that contains the mapping class group, CAT(0) groups, and the fundamental groups of closed 3-manifolds. To accomplish this, we develop a theory of automatic structures on Morse geodesics in Morse local-to-global groups. Other applications of these automatic structures include a description of stable subgroups in terms of regular languages, rationality of the growth of stable subgroups, density in the Morse boundary of the attracting fixed points of Morse elements, and containment of the Morse boundary inside the limit set of any infinite normal subgroup.
