标题： 关于定向4流形上具有唯一扭曲鞍点轨道的NMS流的分类 显示英文标题

标题： Classification of NMS-flows with unique twisted saddle orbit on orientable 4-manifolds

摘要： 研究了在不同一般性假设下，没有不动点的Morse-Smale流（NMS-流）在拓扑等价下的性质。在某些情况下，当周期轨道的数量较少时，可以给出详尽的分类，即列出所有允许此类流的流形，找到拓扑等价的完全不变量，并用某个代表流来描述每个等价类。本文是此类文章系列的延续。 我们考虑了定义在闭合定向4维流形上的具有唯一鞍点轨道的NMS-流，并假设该鞍点轨道是扭曲的。证明了唯一允许这种流的4维流形是流形$\mathbb S^3\times\mathbb S^1$。此外，还确定了这些流正好分为八个拓扑等价类，并为每个等价类构造了一个代表流。 显示英文摘要

摘要： Topological equivalence of Morse-Smale flows without fixed points (NMS-flows) under assumptions of different generalities was studied in a number of papers. In some cases when the number of periodic orbits is small, it is possible to give exhaustive classification, namely to provide the list of all manifolds that admit flows of considered class, find complete invariant for topological equivalence and introduce each equivalence class with some representative flow. This work continues the series of such articles. We consider the class of NMS-flows with unique saddle orbit, under the assumption that it is twisted, on closed orientable 4-manifolds and prove that the only 4-manifold admitting the considered flows is the manifold $\mathbb S^3\times\mathbb S^1$. Also, it is established that such flows are split into exactly eight equivalence classes and construction of a representative for each equivalence class is provided.