论文标题
限制元素和准凸子群的增长
Constricting elements and the growth of quasi-convex subgroups
论文作者
论文摘要
鉴于在地球衡量空间上作用的组$ g $，我们考虑了该空间路径的首选集合（路径系统），并研究了相对指数增长率和无限指数子组的相对指数增长率和$ g $的商人指数增长率，这是与该路径系统有关的Quasi-convex。如果$ g $包含相对于同一路径系统的收缩元素，那么我们就可以确定何时严格小于$ g $的增长率，以及第二种增长率与$ g $的增长率一致。应用程序的示例包括相对双曲线组，$ cat（0）$组和包含摩尔斯元素的双曲线组。
Given a group $G$ acting on a geodesic metric space, we consider a preferred collection of paths of the space -- a path system -- and study the spectrum of relative exponential growth rates and quotient exponential growth rates of the infinite index subgroups of $G$ which are quasi-convex with respect to this path system. If $G$ contains a constricting element with respect to the same path system, we are able to determine when the first kind of growth rates are strictly smaller than the growth rate of $G$, and when the second kind of growth rates coincide with the growth rate of $G$. Examples of applications include relatively hyperbolic groups, $CAT(0)$ groups and hierarchically hyperbolic groups containing a Morse element.
