多顶点2-复形的组合刻划
Combinatorial descriptions of multi-vertex 2-complexes
摘要：
群表示是对只有一个顶点的二维胞腔复形的隐式描述。虽然这样的复形通常足以用于群的拓扑研究，但当焦点转移到几何考虑时，多顶点复形通常是优选的。在这篇文章中，我展示了如何使用传统群表示的一个微小变化来快速描述最重要的多顶点2-复形。作为一个例子，我描述了环面纽结群和单关系子Artin群的多顶点2-复形，它们的基本性质很容易从这些复形导出。后者是用来给一个简单的几何证明的经典结果Appel和Schupp。
英文摘要：
Group presentations are implicit descriptions of 2-dimensional cell complexes with only one vertex. While such complexes are usually sufficient for topological investigations of groups, multi-vertex complexes are often preferable when the focus shifts to geometric considerations. In this article, I show how to quickly describe the most important multi-vertex 2-complexes using a slight variation of the traditional group presentation. As an illustration I describe multi-vertex 2-complexes for torus knot groups and one-relator Artin groups from which their elementary properties are easily derived. The latter are used to give an easy geometric proof of a classic result of Appel and Schupp.
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。
