论文标题
仔细观察$ bs（2,3）$的非律师
A closer look at the non-Hopfianness of $BS(2,3)$
论文作者
论文摘要
Baumslag-solitar $ bs（2,3）$是一个所谓的非人称群体，这意味着它在自身上具有表达$ ϕ $，这不是注入性的。特别是这相当于说$ bs（2,3）$具有同构本身的非平凡商。结果，$ bs（2,3）$的Cayley图具有同构的商，可以使发电机的变化。我们在图形级别上描述了这一商，并仔细研究了最常见的表达$ ϕ $。我们显示其内核是一组无限等级的组，具有明确的发电机集。最后，我们展示了$ ϕ $是如何作为对某些连续地图引起的基本群体的形态而显示的。吉尔伯特·莱维特（Gilbert Levitt）向作者传达了这一观点。
The Baumslag-Solitar group $BS(2,3)$, is a so-called non-Hopfian group, meaning that it has an epimorphism $ϕ$ onto itself, that is not injective. In particular this is equivalent to saying that $BS(2,3)$ has a non-trivial quotient that is isomorphic to itself. As a consequence the Cayley graph of $BS(2,3)$ has a quotient that is isomorphic to itself up to change of generators. We describe this quotient on the graph-level and take a closer look at the most common epimorphism $ϕ$. We show its kernel is a free group of infinite rank with an explicit set of generators. Finally we show how $ϕ$ appears as a morphism on fundamental groups induced by some continuous map. This point of view was communicated to the author by Gilbert Levitt.
