Rauzy型动力学的组合方法II：标号方法和KZB分类定理的第二种证明
A combinatorial approach to Rauzy-type dynamics II: the labelling method and a second proof of the KZB classification theorem
摘要：
劳兹型动力学是对组合对象集合的群作用。第一个也是最著名的例子（劳齐动力学）涉及一个关于排列的作用，与紧致可定向平移曲面上庞加莱映射的区间交换变换（IET）有关。Kontsevich和Zorich以及Boissy通过组合学、代数几何、拓扑学和动力系统的方法对由群作用引起的对象的等价类进行了分类。我们的第一篇论文提出了一个特设的组合证明这种分类。在本文中，我们定义了一个一般的方法，称为标签方法，它允许一个分类劳齐型动力学在一个更系统的方式。我们应用该方法的Rauzy动力学，并获得第二个组合的分类证明。
英文摘要：
Rauzy-type dynamics are group actions on a collection of combinatorial objects. The first and best known example (the Rauzy dynamics) concerns an action on permutations, associated to interval exchange transformations (IET) for the Poincaré map on compact orientable translation surfaces. The equivalence classes on the objects induced by the group action have been classified by Kontsevich and Zorich, and by Boissy through methods involving both combinatorics algebraic geometry, topology and dynamical systems. Our first paper proposed an ad hoc combinatorial proof of this classification. In this paper we define a general method, called the labelling method, which allows one to classify Rauzy-type dynamics in a much more systematic way. We apply the method to the Rauzy dynamics and obtain a second combinatorial proof of the classification.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
