论文标题
Teichmüller和带钉的层压空间
Teichmüller and lamination spaces with pinnings
论文作者
论文摘要
我们描述了由Goncharov--Shen [GS19]引入的模量空间$ \ MATHCAL {p} _ {pgl_2，σ} $的正面和热带点的空间，分别是某些Teichmüller和层压空间，并带有其他数据。在表面$σ$没有穿刺的情况下，我们获得了与Teichmüller空间上各种功能的公式与钉子：$λ$ - 长度，交叉比率坐标和威尔逊线。热带合并图的拓扑描述是根据$ \ Mathcal {p} $ - 层压板给出的。 基于我们对这些“ $ \ MATHCAL {P} $ - 类型”空间的拓扑研究，我们研究了Fock-Goncharov duality的兼容性，地图$ \ Mathbb {i} _ \ Mathcal {a} $ {a} $，$ \ MATHBB { [FG06，FG07，MSW13，GS15]在扩展的集合图下。我们还讨论了手镯底座的融合。
We describe the spaces of the positive and tropical points of the moduli space $\mathcal{P}_{PGL_2,Σ}$ introduced by Goncharov--Shen [GS19] as certain Teichmüller and lamination spaces, respectively, with additional data of pinnings. In the case where the surface $Σ$ has no punctures, we obtain the formulae relating various functions on the Teichmüller space with pinnings: $λ$-lengths, cross ratio coordinates, and Wilson lines. A topological description of the tropicalized amalgamation map is given in terms of $\mathcal{P}$-laminations. Based on our topological study of these "$\mathcal{P}$-type" spaces, we investigate the compatibility of the Fock--Goncharov duality maps $\mathbb{I}_\mathcal{A}$, $\mathbb{I}_\mathcal{X}$ constructed by [FG06,FG07,MSW13,GS15] under the extended ensemble map. We also discuss the amalgamation of bracelet bases.
