论文标题
伪anosovs的班级编号
Class number for pseudo-Anosovs
论文作者
论文摘要
鉴于两种组的$ g $的自动形态，一个人有兴趣知道它们是$ g $的自动形态组中的共轭，还是在$ g $的抽象同源器中，以及这两个属性可能有所不同。当$ g $是可定向表面的基本组时，我们为伪anosov汽车的类别提供了统一的有限定理。我们提供了一个明确的例子，表明了一对属于$ 3 $表面的伪anosov自动形态，它们在映射类组中并非偶联，我们还表明，多余的甲状腺甲甲甲基甲甲型甲状腺具有无限的独立自动形态，具有类别的类别。在附录中，我们简要调查了latimer-macduffee定理，该定理涉及$ \ mathbb {z}^n $的自动形态案例，其观点适合与表面组自动形态的类比。
Given two automorphisms of a group $G$, one is interested in knowing whether they are conjugate in the automorphism group of $G$, or in the abstract commensurator of $G$, and how these two properties may differ. When $G$ is the fundamental group of a closed orientable surface, we present a uniform finiteness theorem for the class of pseudo-Anosov automorphisms. We present an explicit example of a commensurably conjugate pair of pseudo-Anosov automorphisms of a genus $3$ surface, that are not conjugate in the Mapping Class Group, and we also show that infinitely many independent automorphisms of hyperbolic orbifolds have class number equal to one. In the appendix, we briefly survey the Latimer-MacDuffee theorem that addresses the case of automorphisms of $\mathbb{Z}^n$, with a point of view that is suited to an analogy with surface group automorphisms.
