标题： 有界$\mathfrak{sp}_4$-层和它们的相交坐标 显示英文标题

标题： Bounded $\mathfrak{sp}_4$-laminations and their intersection coordinates

摘要： 我们引入在标记曲面$\boldsymbol{\Sigma}$上的有理有界$\mathfrak{sp}_4$-层作为 Fock--Goncharov 模空间 [FG06] 的有理热带点$\mathcal{A}_{Sp_4,\boldsymbol{\Sigma}}(\mathbb{Q}^{\mathsf{T}})$的拓扑模型。我们的空间由 Kuperberg [Kup96] 引入的某些$\mathfrak{sp}_4$-网的等价类以及有理测度组成。我们使用 Shen--Sun--Weng [SSW25] 的交数的$\mathfrak{sp}_4$情况定义热带坐标系，并利用分 graded$\mathfrak{sp}_4$- skein 代数的框架建立双射。这为 Fock--Goncharov 对偶性对于$\mathfrak{sp}_4$提供了拓扑视角。 显示英文摘要

摘要： We introduce rational bounded $\mathfrak{sp}_4$-laminations on a marked surface $\boldsymbol{\Sigma}$ as a proposed topological model for the rational tropical points $\mathcal{A}_{Sp_4,\boldsymbol{\Sigma}}(\mathbb{Q}^{\mathsf{T}})$ of the Fock--Goncharov moduli space [FG06]. Our space consists of certain equivalence classes of $\mathfrak{sp}_4$-webs introduced by Kuperberg [Kup96], together with rational measures. We define tropical coordinate systems using the $\mathfrak{sp}_4$-case of the intersection number of Shen--Sun--Weng [SSW25], and establish a bijection using the framework of the graded $\mathfrak{sp}_4$-skein algebra. This provides a topological perspective for Fock--Goncharov duality for $\mathfrak{sp}_4$.