论文标题
通过热带群集转换的伪anosov映射类的表征
A characterization of pseudo-Anosov mapping classes via tropical cluster transformations
论文作者
论文摘要
我们纯粹是根据剪切坐标中的表达方式来表征通用伪-Anosov映射类，从而回答了Papadopoulos-Penner提出的问题[PP93]。该表征具有一个群集代数概括，称为[IK21]中引入的符号稳定性。通过与[IK21]中的结果结合使用，我们看到群集$ \ Mathcal {a} $的代数熵和$ \ Mathcal {x} $ - 由通用的Pseudo-Anosov映射类引起的转换均与其拓扑结合。
We give a characterization of generic pseudo-Anosov mapping classes purely in terms of their expressions in the shear coordinates, thus giving an answer to a problem raised by Papadopoulos--Penner [PP93]. This characterization has a cluster algebraic generalization called the sign stability introduced in [IK21]. By combining with the results in [IK21], we see that the algebraic entropies of the cluster $\mathcal{A}$- and $\mathcal{X}$-transformations induced by a generic pseudo-Anosov mapping class both coincide with its topological entropy.
