通过热带簇变换刻画伪Anosov映射类
几何拓扑
2024-12-30 v3 组合数学
动力系统
摘要
我们纯粹依据剪切坐标中的表达式给出了一般伪Anosov映射类的刻画，从而回答了Papadopoulos--Penner [PP93]提出的一个问题。这一刻画具有一种称为符号稳定性的簇代数推广，该概念在[IK21]中引入。结合[IK21]中的结果，我们看到由一般伪Anosov映射类诱导的簇-与-变换的代数熵均与其拓扑熵一致。
引用
@article{arxiv.2010.05214,
title = {A characterization of pseudo-Anosov mapping classes via tropical cluster transformations},
author = {Tsukasa Ishibashi and Shunsuke Kano},
journal= {arXiv preprint arXiv:2010.05214},
year = {2024}
}
备注
Previous title is "Sign stability of mapping classes on marked surfaces I: empty boundary case". Compare to the previous paper, the review part is simplified and the characterization is concentrated on the "generic" pA