论文标题
标记表面上映射类的标志稳定性II：通过减少的一般情况
Sign stability of mapping classes on marked surfaces II: general case via reductions
论文作者
论文摘要
我们给出了沿多个构图类映射类的减少过程的集群代数描述。基于此描述，我们根据均匀标志稳定性的较弱版本的形式在一般标记的表面上表征了伪-Anosov映射类，从而在上一篇论文[IK20]中推广了主要结果。此外，我们将突变回路的一般还原过程参数化，这是由热带聚类$ \ MATHCAL {x} $的合理多面体锥体参数化的，其中包括沿多繁殖的还原和[ISH19]中引入的群集还原。
We give a cluster algebraic description of the reduction procedure of mapping classes along a multicurve. Based on this description, we characterize pseudo-Anosov mapping classes on a general marked surface in terms of a weaker version of the uniform sign stability, generalizing the main result in the previous paper [IK20]. Moreover we axiomatize a general reduction procedure of mutation loops parametrized by a rational polyhedral cone in the tropical cluster $\mathcal{X}$-variety, which includes both the reduction along a multicurve and the cluster reduction introduced in [Ish19].
