曲面上曲线相交问题及推广

项目的核心问题是曲面上闭路的交点与自交点数, 我们拟采用Nielsen不动点理论的方法将交点分类, 利用Grobner基理论进行分类判别,给出交点数的代数计算方法。 在此基础上，计算更多的与闭路交点相关的低维拓扑学中的不变量，如Heegaard距离等。同时,我们也寻找用交点来刻画低维流形及相互关系的不变量。

Our crucial problem in consideration of this project is the intersection and self-intersection of loops on surfaces. By using Nielsen fixed point theory, we divide intersections into some classes and decide the classification with a help of Grobner basis. An algorithm to compute intersection will be given. Based on such an algorithm we try to compute more invariants in low-dimensional topology, such as Heegaard distance, related to the intersections of loops. Meanwhile, we also look for new invariants based on intersections to describe low-dimensional manifolds and their relations.