论文标题
双曲线组的组和外部自动形态图表上的火车轨道
Train Tracks on Graphs of Groups and Outer Automorphisms of Hyperbolic Groups
论文作者
论文摘要
Stallings指出，自由组的外部自动形态可能被认为是图形的细分，然后是一系列褶皱。在本论文中，我们证明，满足这种情况的基本图的基本组的自动形态可以用Bestvina handel的意义来代表不可减至的火车轨道图（我们允许不变的子分类崩溃）。当然，我们还构建了相对火车轨道图。在此过程中，我们对作用在树木上的群体，群体形态及其折叠的群体的贝司列理论进行了新的阐述。我们为自由产品的自动形态产生正常形式，并扩展了清 - rafi的论点，以表明它们不是准晶格。作为一种应用，我们肯定地回答了Paulin的问题：有限生成的单词双曲线群的外部自动形态满足了一种动态的三分法，将Nielsen-Thurston概括为“周期性，还原，可还原或伪anosov”。在论文的结尾，我们收集了一些开放问题，我们发现有趣的问题。
Stallings remarked that an outer automorphism of a free group may be thought of as a subdivision of a graph followed by a sequence of folds. In this thesis, we prove that automorphisms of fundamental groups of graphs of groups satisfying this condition may be represented by irreducible train track maps in the sense of Bestvina-Handel (we allow collapsing invariant subgraphs). Of course, we construct relative train track maps as well. Along the way, we give a new exposition of the Bass-Serre theory of groups acting on trees, morphisms of graphs of groups, and foldings thereof. We produce normal forms for automorphisms of free products and extend an argument of Qing-Rafi to show that they are not quasi-geodesic. As an application, we answer affirmatively a question of Paulin: outer automorphisms of finitely-generated word hyperbolic groups satisfy a dynamical trichotomy generalizing the Nielsen-Thurston "periodic, reducible or pseudo-Anosov." At the end of the thesis we collect some open problems we find interesting.
