几何群论中的仙人掌群
Cactus groups from the viewpoint of geometric group theory
摘要：
仙人掌群及其纯子群出现在数学的各个领域，目前正吸引着不同数学社区的注意力。它们与直角Coxeter群和辫群都有相似之处。在这篇文章中，我们的目标是突出几何群论为研究这些群体提供的工具。在新的贡献可能由于这种几何的角度来看，我们描述了一个明确的和有效解的共轭问题，我们证明了仙人掌群几乎是特殊的协紧和acylindrically双曲。
英文摘要：
Cactus groups and their pure subgroups appear in various fields of mathematics and are currently attracting attention from diverse mathematical communities. They share similarities with both right-angled Coxeter groups and braid groups. In this article, our goal is to highlight the tools offered by geometric group theory for the study of these groups. Among the new contributions made possible thanks to this geometric perspective, we describe an explicit and efficient solution to the conjugacy problem, and we prove that cactus groups are virtually cocompact special and acylindrically hyperbolic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
