Nielsen约化与弦滑群胚的多边形视角
几何拓扑
2010-10-29 v2
摘要
Nielsen约化是一种将自由群的任何自同态分解为初等Nielsen变换乘积的算法。虽然这可以应用于具有一个边界分支的曲面的映射类，但所得分解通常不具有拓扑解释。在这篇综述中，我们讨论了一种称为fatgraph Nielsen约化的变体，它将这种映射类分解为初等Nielsen变换，这些变换被解释为的多边形域的重新排列，由中的弧系描述。这些初等变换生成了的弦滑群胚，我们对其进行了综述，并用生成元和关系进行了描述。
引用
@article{arxiv.1010.5275,
title = {A Polygonal Perspective of Nielsen Reduction and the Chord Slide Groupoid},
author = {Alex James Bene},
journal= {arXiv preprint arXiv:1010.5275},
year = {2010}
}
备注
This survey (minus minor corrections) was written for and published in the abstracts for the 57th Topology Symposium which took place in Okayama, JP \emph{2010}. It summarizes the contents of a talk of the same title which was given by the author at that conference on \emph{8/12/2010}