改进的Seifert算法的纽结可视化

纽结或链环的Seifert曲面是可定向曲面,关于该曲面的原理图可以在纽结理论的教材上查阅到,但是仅知道这些,想要去了解它们的形状和结构,仍然是很困难的.将讨论纽结和链环的可视化算法,包括Seifert算法和基于编织命名法的可视化算法,最后,给出了改进后的Seifert算法,另外,对纽结和链环生成的可定向闭曲面的亏格也做了进一步地研究.

Visualization of knots based on improved Seifert's algorithm

A Seifert surface of a knot or link is an oriented surface,schematic images of these surfaces are shown in every text book on knot theory,but from these it is hard to understand their shape and structure.The methods of the visualization of such surfaces is discussed,such as Seifert's algorithm and braid representation.Finally,an improved Seifert's algorithm is given,then the genus of the oriented and closed surface are further studied.