论文标题
用两个鞍形图可视化摩尔斯流动的3球图
Visualization of Morse flow with two saddles on 3-sphere diagrams
论文作者
论文摘要
我们描述了摩尔斯 - 男性流的所有可能的拓扑结构，而没有在三维球体上没有封闭轨迹的情况，这些球体有两个来源，两个水槽，一个摩尔斯索引1，一个摩尔斯索引2的鞍座，不超过10个鞍座连接。为了对此类流进行分类，使用了广义的Heegaard图或Pr-Dagram，在这种情况下，该图由一个球体和两个封闭的曲线组成，其相交点对应于鞍座连接。我们已经发现了所有可能的，直到同态性，是将两个圆圈嵌入不超过10点横向相交并构建其平面可视化的2个圆形的方法。
We describe all possible topological structures of Morse-Smale flows without closed trajectories on a three-dimensional sphere, which have two sources, two sinks, one saddle of Morse index 1, one saddle of Morse index 2, and no more than 10 saddle connections. To classify such flows, a generalized Heegaard diagram or Pr-diagram is used, which in this case consists of a sphere and two closed curves, the intersection points of which correspond to saddle connections. We have found all possible, up to homeomorphism, ways to embed two circles in a 2-sphere with no more than 10 points of transversal intersection and construct its planar visualisations.
