论文标题
扭曲的马鞍轨道的非环形流动环境的拓扑
Topology of Ambient 3-Manifolds of Non-singular Flows with Twisted Saddle Orbit
论文作者
论文摘要
在本文中，在流动的周期性轨道中，只有一个鞍座，并且考虑了扭曲的假设。获得了这种歧管拓扑拓扑的详尽描述。也就是说，已经确定，任何承认这种流量的歧管都是镜头空间，也可以是带有射影空间的镜头空间的连接总和，或者具有基本同构的seifert歧管，与球体的基本同构和三个奇异纤维。由于后者是简单的歧管，因此获得的结果反驳了这样的结果，即在简单的歧管中，所考虑的流量仅接受镜头空间。
In the present paper, non-singular Morse-Smale flows on closed orientable 3-manifolds under the assumption that among the periodic orbits of the flow there is only one saddle one and it is twisted are considered. An exhaustive description of the topology of such manifolds is obtained. Namely, it has been established that any manifold admitting such flows is either a lens space, or a connected sum of a lens space with a projective space, or Seifert manifolds with base homeomorphic to sphere and three singular fibers. Since the latter are simple manifolds, the result obtained refutes the result that among simple manifolds, the considered flows admit only lens spaces.
