论文标题
女孩表面上最佳流动的拓扑结构
Topological structure of optimal flows on the Girl's surface
论文作者
论文摘要
我们研究了女孩表面上流的拓扑结构，这是射传中的两个可能的沉浸在三维空间中，并具有自我发射的三个点。首先，我们描述了男孩和女孩表面的细胞结构，并证明了项目平面的独特图像以2盘形式的形式，其中确定了边界的相反点，并且该边界属于表面1骨的预先形象。其次，我们描述了三个具有一个固定点的流程结构，在女孩的表面上没有分离，并证明没有其他这样的流。第三，我们证明了莫尔斯 - 山的流动，而且它们在男孩和女孩的表面上在结构上是稳定的。第四，我们发现了女孩表面上最佳的摩尔斯男友流量的所有可能结构。第五，我们在投影平面上获得了莫尔斯 - 摩尔流的分类，并沉浸在女孩的表面上。最后，我们描述了这些流集的线性连通性的组成部分
We investigate the topological structure of flows on the Girl's surfaces which is one of two possible immersions of the projective plane in three-dimensional space with one triple point of the selfintersection. First, we describe the cellular structure of the Boy's and Girl's surfaces and prove that there are unique images of the project plane in the form of a 2-disc, in which the opposite points of the boundary are identified and this boundary belongs to the preimage of the 1-skeleton of the surface. Second, we described three structures of flows with one fixed point and no separatrix on the Girl's surface and proved that there are no other such flows. Third, we proved that Morse-Smale flows and they alone are structurally stable on the Boy's and Girl's surfaces. Fourth, we have found all possible structures of optimal Morse-Smale flows on the Girl's surface. Fifth, we have obtained a classification of Morse-Smale flows on the projective plane, that immersed on the Girl's surface. And finally, we described the components of linear connectivity of sets of these flows
