论文标题
限制自由团体自动形态的树木：普遍性
Limit trees for free group automorphisms: universality
论文作者
论文摘要
对于任何自由组自动形态，我们将一个限制树的通用（锥）与三个定义特性相关联：首先，该树具有自由组的最小等距动作，具有微不足道的弧形稳定器；其次，树木的独特扩张代表了自由群体的自动形态。最后，Loxodromic元素恰恰是弱限制的元素，这些要素主要限制了自动形态学下的层压效果。因此，对树上的动作检测到自动态的主导指数动力学。 作为推论，我们先前构建的检测指数动力学的极限是规范。我们还表征了所有非常小的树木，这些树木承认代表给定的自动形态的同性恋不断扩展。在附录中，我们证明了Feighn-Handel识别定理的atoroidal外部自动形态学的变化。
To any free group automorphism, we associate a universal (cone of) limit tree(s) with three defining properties: first, the tree has a minimal isometric action of the free group with trivial arc stabilizers; second, there is a unique expanding dilation of the tree that represents the free group automorphism; and finally, the loxodromic elements are exactly the elements that weakly limit to dominating attracting laminations under forward iteration by the automorphism. So the action on the tree detects the automorphism's dominating exponential dynamics. As a corollary, our previously constructed limit pretree that detects the exponential dynamics is canonical. We also characterize all very small trees that admit an expanding homothety representing a given automorphism. In the appendix, we prove a variation of Feighn--Handel's recognition theorem for atoroidal outer automorphisms.
