多分支闭曲线的虚拟字符串
几何拓扑
2007-05-23 v3
摘要
Gauss 段是某曲面上具有多分支的泛闭曲线的组合表述。虚拟字符串是一组带有箭头的圆周，表示此类曲线的交叉点。每条闭曲线都有一个底层的虚拟字符串，而每个虚拟字符串都有一个底层的 Gauss 段。字式划分是 Gauss 段的字母表集合的一个划分，满足关于该 Gauss 段的特定条件。在本文中，我们利用虚拟字符串理论，通过 Gauss 段和字式划分给出 2-球面（从而也是 2 维欧氏空间）中闭曲线的组合描述。
引用
@article{arxiv.math/0412023,
title = {Virtual Strings for Closed Curves with Multiple Components},
author = {William J. Schellhorn},
journal= {arXiv preprint arXiv:math/0412023},
year = {2007}
}
备注
35 pages, 5 figures. No fundamental changes were made between the second and third versions. The third version contains some clarifications in the definitions and proofs that will hopefully improve understanding