论文标题
仙人掌群从几何群体理论的角度来看
Cactus groups from the viewpoint of geometric group theory
论文作者
论文摘要
仙人掌群及其纯粹的亚组出现在数学的各个领域，目前正在吸引各种数学社区的关注。他们与右角的高级群组和辫子组都有相似之处。在本文中，我们的目标是强调几何群体理论为这些群体研究提供的工具。在通过这种几何视角的新作用中，我们可以做出明确，有效的解决方案，并证明仙人掌基团实际上是特殊和酰基糖的双曲线。
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.
