发表机构
Institute of Mathematics of the Polish Academy of Sciences; Department of Mathematics School of Mathematical Sciences Ramakrishna Mission Vivekananda Educational & Research Institute (RKMVERI); Department of Mathematics, Adams State University; HUN-REN Alfréd Rényi Institute of Mathematics（波兰科学院数学研究所; 罗摩克里希那使命维韦卡南达教育与研究机构; 阿达姆斯州立大学数学系; 匈牙利研究与创新网络阿尔弗雷德·雷尼数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究开发两种从边界动力学证明无限围长的方法，结合 Nakamura 准则得到相关群及作用的无限围长结果，还证明有限生成 large 群均有无限围长，解答了他人提出的问题。
AI 中文摘要
我们开发了两种从边界动力学证明无限围长的方法。第一种，利用拓扑自由的极端边界作用，为有限生成的 acylindrically 双曲群给出了边界动力学视角的无限围长证明。第二种，将 Nakamura 准则分别与旗空间和 Roller 边界动力学结合，得到半单 S-代数群以及有限维、第二可数、非欧 CAT(0) 立方复形上本质非初等作用的无限围长结果。我们还证明，每个有限生成的 large 群都具有无限围长，从而回答了 Akhmedov 和 Mishra 提出的问题。
英文摘要
We develop two methods for proving infinite girth from boundary dynamics. First, we use topologically free extreme boundary actions to give a boundary-dynamical proof of infinite girth for finitely generated acylindrically hyperbolic groups. The second combines Nakamura's criterion with, respectively, flag-space and Roller-boundary dynamics, yielding infinite-girth results for semisimple $S$-algebraic groups and for essential non-elementary actions on finite-dimensional, second countable, non-Euclidean CAT(0) cube complexes. We also prove that every finitely generated large group has infinite girth, thereby answering a question of Akhmedov and Mishra.
Comments24 pages, preliminary version. Comments are welcome
