论文标题
简单的Smale流及其模板在$ s^3 $上
Simple Smale flows and their templates on $S^3$
论文作者
论文摘要
嵌入式模板是用于模拟结和链接的动力学的几何工具，作为$ 3 $维流量的周期性轨道。我们证明，对于带有固定同构类型的$ s^3 $中的嵌入式模板，其作为三价空间图的边界是完整的同位素不变的。此外，我们通过Kauffman的空间图构建了一个嵌入式模板的不变，这是一组结和链接。作为应用程序，讨论了简单的Smale流量的同位素分类。
The embedded template is a geometric tool in dynamics being used to model knots and links as periodic orbits of $3$-dimensional flows. We prove that for an embedded template in $S^3$ with fixed homeomorphism type, its boundary as a trivalent spatial graph is a complete isotopic invariant. Moreover, we construct an invariant of embedded templates by Kauffman's invariant of spatial graphs, which is a set of knots and links. As application, the isotopic classification of simple Smale flows on $S^3$ is discussed.
