一次加边曲面的映射类群的弦图表示
A Chord Diagrammatic Presentation of the Mapping Class Group of a Once Bordered Surface
摘要：
Ptolemy广群是一个组合广群，它是由标记三价胖图上的基本移动生成的，具有三种关系。通过Teichmüller空间的胖图分解，证明了Ptolemy广群是Teichmüller空间的基本路广群的一个映射类群等变子群，其对象为一个离散集.特别是，它导致一个无限的，但组合简单，介绍了映射类群的可定向曲面。本文以弦滑为生成元，利用五种关系，用标记线性弦图给出了具有一个边界分支的可定向曲面的Ptolemy广群的全映射类群等变子广群.我们还介绍了这种演示文稿的双重版本，它具有某些应用程序的优势，其中之一是。
英文摘要：
The Ptolemy groupoid is a combinatorial groupoid generated by elementary moves on marked trivalent fatgraphs with three types of relations. Through the fatgraph decomposition of Teichmüller space, the Ptolemy groupoid is a mapping class group equivariant subgroupoid of the fundamental path groupoid of Teichmüller space with a discrete set objects. In particular, it leads to an infinite, but combinatorially simple, presentation of the mapping class group of an orientable surface. In this note, we give a presentation of a full mapping class group equivariant subgroupoid of the Ptolemy groupoid of an orientable surface with one boundary component in terms of marked linear chord diagrams, with chord slides as generators and five types of relations. We also introduce a dual version of this presentation which has advantages for certain applications, one of which is given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
