论文标题
结是摩尔斯 - 梅尔三型摩尔型摩尔斯 - 摩尔三型近形形态的完全不变的结构
Knot as a complete invariant of a Morse-Smale 3-diffeomorphism with four fixed points
论文作者
论文摘要
镜头空间是仅有的3个manifolds，可以接受四个固定点的梯度样流。这是莫尔斯不平等和摩尔斯的功能的直接推论，具有四个关键点。对于梯度样的差异性的类似问题是开放的。可以通过描述一系列考虑的差异性和构造每个共轭类别的代表性差异类别的完整拓扑结合，并通过抽象不变性的类别构建代表性的差异性。 ch。 Bonnati和V. Z. Grines证明，莫尔斯 - 摩尔语流的拓扑结合类别与独特的鞍座的拓扑结合类是由$ \ Mathbb s^2 \ s^2 \ times \ times \ mathbb s^1 $的等价类别定义三维领域。在本文中，对于恰好有两个鞍点和独特的异斜曲线的梯度样的差异性，获得了相似的结果。
Lens spaces are the only 3-manifolds that admit gradient-like flows with four fixed points. This is an immediate corollary of Morse inequality and of the Morse function with four critical points existence. A similar question for gradient-like diffeomorphisms is open. Solution can be approached by describing a complete topological conjugacy invariant of the class of considered diffeomorphisms and constructing of representative diffeomorphism for every conjugacy class by the abstract invariant. Ch. Bonnati and V. Z. Grines proved that the topological conjugacy class of Morse-Smale flows with unique saddle is defined by the equivalence class of the Hopf knot in $\mathbb S^2\times\mathbb S^1$ which is projection of one-dimensional saddle separatrice and used the mentioned approach to prove that the ambient manifold of a diffeomorphism of this class is the three-dimensional sphere. In the present paper similar result is obtained for the gradient-like diffeomorphisms with exactly two saddle points and the unique heteroclinic curve.
