论文标题
BESTVINA-BRADY群体和RAAG识别问题的BNS-Invariants的图形描述
A graphical description of the BNS-invariants of Bestvina-Brady groups and the RAAG recognition problem
论文作者
论文摘要
一个有限的BESTVINA-BRADY团体（BBG）承认仅涉及换向者的演讲。我们表明，如果图形允许某种类型的跨越树，那么相关的BBG是一个直角的Artin组（RAAG）。作为一个应用程序，我们获得了BBG类包含RAAG类的类别。另一方面，我们提供了一个标准，以证明某些有限的BBG并非对RAAGS（或更一般的Artin组）的同构。这是基于对有限呈现的BBG的Bieri-Neumann-strebel不变的描述，该bbgs在分离子图的角度（类似于RAAGS）。作为一个应用，我们表征了与二维标志复合物相关的BBG何时在某些子图方面是一种RAAG。
A finitely presented Bestvina-Brady group (BBG) admits a presentation involving only commutators. We show that if a graph admits a certain type of spanning trees, then the associated BBG is a right-angled Artin group (RAAG). As an application, we obtain that the class of BBGs contains the class of RAAGs. On the other hand, we provide a criterion to certify that certain finitely presented BBGs are not isomorphic to RAAGs (or more general Artin groups). This is based on a description of the Bieri-Neumann-Strebel invariants of finitely presented BBGs in terms of separating subgraphs, analogous to the case of RAAGs. As an application, we characterize when the BBG associated to a 2-dimensional flag complex is a RAAG in terms of certain subgraphs.
