论文标题
图形辫子组的分组分解图
Graph of groups decompositions of graph braid groups
论文作者
论文摘要
我们提供了一个明确的结构，该结构使人们可以轻松地将图形编织组作为组图分解。这使我们能够计算各种图形的辫子组，并为图形编织组提供两个通用标准，以将其分为非平凡的免费产品，回答了Genevois的两个问题。我们还使用它来区分某些右角的Artin组和图形编织组。此外，我们提供了一个相对双曲线的图形编织组的明确示例，但相对于适当的子图的编织组而言不是双曲线。这回答了Genevois的另一个问题。
We provide an explicit construction that allows one to easily decompose a graph braid group as a graph of groups. This allows us to compute the braid groups of a wide range of graphs, as well as providing two general criteria for a graph braid group to split as a non-trivial free product, answering two questions of Genevois. We also use this to distinguish certain right-angled Artin groups and graph braid groups. Additionally, we provide an explicit example of a graph braid group that is relatively hyperbolic, but is not hyperbolic relative to braid groups of proper subgraphs. This answers another question of Genevois in the negative.
