论文标题
带有合同元素的小组动作的大型商
Large quotients of group actions with a contracting element
论文作者
论文摘要
对于非优质组$ g $在适当的地理公制空间上的任何适当行动，我们表明，如果$ g $包含合同元素，则存在一系列适当的商组，其增长率趋向于$ g $的增长率。对于合同元素的适当行动的产品也获得了类似的陈述。 本文所涉及的工具包括用于建造大树的扩展引理，F。Dahmani，V。Guirardel和D. Osin开发的旋转家庭理论，以及由M. Bestvina，K。Bromberg和K. Fujiwara引入的标准公制空间的准树木。给CAT（0）组和映射课程组提供了几种应用。
For any proper action of a non-elementary group $G$ on a proper geodesic metric space, we show that if $G$ contains a contracting element, then there exists a sequence of proper quotient groups whose growth rate tends to the growth rate of $G$. Similar statements are obtained for a product of proper actions with contracting elements. The tools involved in this paper include the extension lemma for the construction of large tree, the theory of rotating families developed by F. Dahmani, V. Guirardel and D. Osin, and the construction of a quasi-tree of metric spaces introduced by M. Bestvina, K. Bromberg and K. Fujiwara. Several applications are given to CAT(0) groups and mapping class groups.
