Probing mapping class groups using arcs
Probing mapping class groups using arcs
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使用弧探测映射类组
DOI：
10.1090/pspum/074/2264535
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
R. Penner
中科院分区：
文献类型：
--
作者：
R. Penner
本文讨论了曲面的映射类群在曲面上不相交嵌入曲线或圆弧的同伦类集合上的作用，以此作为理解黎曼模空间及其拓扑和几何不变量的工具。此外，所有这些同伦类的曲线或圆弧的集合的适当的补全、推演或商给出了Teichm-Uller空间的瑟斯顿边界或模空间的脂肪图的组合描述，并讨论了相关的公开问题和问题。
The action of the mapping class group of a surface on the collection of homotopy classes of disjointly embedded curves or arcs in the surface is discussed here as a tool for understanding Riemann's moduli space and its topological and geometric invariants. Furthermore, appropriate completions, elaborations, or quotients of the set of all such homotopy classes of curves or arcs give for instance Thurston's boundary for Teichm\"uller space or a combinatorial description of moduli space in terms of fatgraphs. Related open problems and questions are discussed.