Knot theory of ℝ‐covered Anosov flows: homotopy versus isotopy of closed orbits
Knot theory of ℝ‐covered Anosov flows: homotopy versus isotopy of closed orbits
复制标题
ℝ覆盖的阿诺索夫流的结理论：闭合轨道的同伦与同位素
DOI：
10.1112/jtopol/jtt041
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发表时间：
2012
影响因子：
1.1
通讯作者：
Sérgio R. Fenley
中科院分区：
文献类型：
--
作者：
Thomas Barthelm'e;Sérgio R. Fenley
在这篇文章中，我们研究了紧致三维流形中由周期轨道覆盖的Anosov流实现的节点。我们证明，如果两个轨道是自由同伦的，那么实际上他们是同位素。我们表明，电梯的周期轨道的普遍覆盖是unknotted。当流形是超环面的，我们推导出一些更精细的性质有关的存在性嵌入圆柱连接两个给定的同伦轨道。
In this article, we study the knots realized by periodic orbits of ℝ‐covered Anosov flows in compact three‐manifolds. We show that if two orbits are freely homotopic, then in fact they are isotopic. We show that lifts of periodic orbits to the universal cover are unknotted. When the manifold is atoroidal, we deduce some finer properties regarding the existence of embedded cylinders connecting two given homotopic orbits.