The structure of branching in Anosov flows of 3-manifolds
The structure of branching in Anosov flows of 3-manifolds
复制标题
3 流形 Anosov 流中的分支结构
DOI：
--
复制
发表时间：
1994
期刊：
影响因子：
--
通讯作者：
Sérgio R. Fenley
中科院分区：
文献类型：
--
作者：
Sérgio R. Fenley
抽象。本文研究三维流形中Anosov流的拓扑。具体来说，我们认为电梯的普遍覆盖的稳定和不稳定的叶理，并分析这些叶理的叶空间。我们完全确定了这些叶空间中的非Hausdorff点的结构。有很多后果：（1）当叶空间为非Hausdorff空间时，流形中存在自由同伦的闭轨;（2）在拓扑共轭下，悬挂Anosov流是唯一的闭轨之间不存在自由同伦的Anosov流;（3）当存在无穷多个稳定叶空间时，（在通用覆盖中）彼此不分离，然后我们在流形中产生一个环面，它横向于Anosov流，因此是不可压缩的，（4）给出双曲流形中的非Hausdorff例子，并推导出泛覆盖中稳定/不稳定叶的极限集的重要性质。
Abstract. In this article we study the topology of Anosov flows in 3-manifolds. Specifically we consider the lifts to the universal cover of the stable and unstable foliations and analyze the leaf spaces of these foliations. We completely determine the structure of the non Hausdorff points in these leaf spaces. There are many consequences: (1) when the leaf spaces are non Hausdorff, there are closed orbits in the manifold which are freely homotopic, (2) suspension Anosov flows are, up to topological conjugacy, the only Anosov flows without free homotopies between closed orbits, (3) when there are infinitely many stable leaves (in the universal cover) which are non separated from each other, then we produce a torus in the manifold which is transverse to the Anosov flow and therefore is incompressible, (4) we produce non Hausdorff examples in hyperbolic manifolds and derive important properties of the limit sets of the stable/unstable leaves in the universal cover.