论文标题
关于有限呈现的Bestvina-Brady群体的结构
On the structure of finitely presented Bestvina-Brady groups
论文作者
论文摘要
由于其几何，组合和算法的特性，右角ARTIN组及其子组引起了极大的兴趣。使用有限的简单图定义这些组很方便。组的同构类型由图唯一确定。此外，可以根据其定义图来表达许多直角artin组的结构特性。 在本文中，我们解决了理解右角Artin组的一类子组的结构的问题。 Bestvina和Brady在他们的开创性工作中研究了这些亚组（现在称为Bestvina-Brady群体或Artin内核），从有限的条件观点研究。与右角的ARTIN组不同，BestVina-Brady组的同构类型并非由定义图确定。我们证明，某些有限的BestVina-Brady群体可以表示为迭代合并产品。此外，我们表明可以从定义环境右角Artin组的图表中读取这种合并产品。
Right-angled Artin groups and their subgroups are of great interest because of their geometric, combinatorial and algorithmic properties. It is convenient to define these groups using finite simplicial graphs. The isomorphism type of the group is uniquely determined by the graph. Moreover, many structural properties of right angled Artin groups can be expressed in terms of their defining graph. In this article we address the question of understanding the structure of a class of subgroups of right-angled Artin groups in terms of the graph. Bestvina and Brady, in their seminal work, studied these subgroups (now called Bestvina-Brady groups or Artin kernels) from a finiteness conditions viewpoint. Unlike the right-angled Artin groups the isomorphism type of Bestvina-Brady groups is not uniquely determined by the defining graph. We prove that certain finitely presented Bestvina-Brady groups can be expressed as an iterated amalgamated product. Moreover, we show that this amalgamated product can be read off from the graph defining the ambient right-angled Artin group.
