可定向曲面上的一类闭曲线系统

A Closed Curve System on the Orientable Surface

利用组合数学的思想、拓扑的方法研究在可定向曲面上,一类含有个数最多的不可收缩的、两两不相交、互不同伦的圈(闭曲线)系统及其性质,得出了关于这些圈的一些拓扑定性性质,并给出这些圈在曲面上的位置分布.

Using combinatorial thoughts and topological methods,a closed curve system that contains the most number of non-contractible,pair-wise disjoint and pair-wise non-homotopic closed curves on the orientable surface is investigated.Some topological qualitative characteristics are obtained.Moreover,the position of those curves are shown.