论文标题
自由组内态的动力和几何形状
The dynamics and geometry of free group endomorphisms
论文作者
论文摘要
我们证明，自由组的上升HNN扩展是且仅当他们没有Baumslag-Solitar子组时。这扩展了Brinkmann的定理，即当且仅当他们没有自由的Abelian子组等级2的情况下，自由循环的群体是单词hyperbolic。该论文分为两个独立部分： 1）我们研究了自由组的注射性非物质内态性的动力学。我们证明了一种规范定理，该定理初始化了改进的内态相对火车轨道的发展；这种结构定理具有独立的兴趣，因为它提出了许多关于可涉及的注射性内态性的开放问题。 2）作为结构定理的应用，我们能够（相对）将Brinkmann的定理与以前的工作相结合，并获得上述主要结果。在最后一部分中，我们将结果进一步扩展到自由因素的自由组扩展。
We prove that ascending HNN extensions of free groups are word-hyperbolic if and only if they have no Baumslag-Solitar subgroups. This extends the theorem of Brinkmann that free-by-cyclic groups are word-hyperbolic if and only if they have no free abelian subgroups of rank 2. The paper is split into two independent parts: 1) We study the dynamics of injective nonsurjective endomorphisms of free groups. We prove a canonical structure theorem that initializes the development of improved relative train tracks for endomorphisms; this structure theorem is of independent interest since it makes many open questions about injective endomorphisms tractable. 2) As an application of the structure theorem, we are able to (relatively) combine Brinkmann's theorem with our previous work and obtain the main result stated above. In the final section, we further extend the result to HNN extensions of free groups over free factors.
