Pseudo-Anosov Flows and Incompressible Tori
Pseudo-Anosov Flows and Incompressible Tori
复制标题
伪阿诺索夫流和不可压缩环面
DOI：
--
复制
发表时间：
2003
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
我们研究了支持伪Anosov流的3-流形中的不可压缩环面，以及这种流形的基本群的更一般的Z- ⊕ Z子群。如果这个子群中没有元素可以用伪Anosov流的闭轨来表示，我们证明了这个流与环面的Anosov微分同态的悬挂拓扑共轭。具体地说，它是非奇异的，是阿诺索夫流。由此可以得出，要么伪Anosov流与悬浮Anosov流拓扑共轭，要么任何浸没的不可压缩环面都可以实现为从流的闭轨到自身的自由同伦。关键工具是分析非Hausdorff树上的群操作，也称为R-序树--我们在自由操作的情况下产生一个不变轴。这些结果的一个应用如下：假设流形有一个横跨伪Anosov流的R-覆盖的叶状结构。如果流不是R-覆盖的Anosov流，那么它得出流形是阿托洛夫的。
We study incompressible tori in 3-manifolds supporting pseudo-Anosov flows and more generally Z ⊕ Z subgroups of the fundamental group of such a manifold. If no element in this subgroup can be represented by a closed orbit of the pseudo-Anosov flow, we prove that the flow is topologically conjugate to a suspension of an Anosov diffeomorphism of the torus. In particular it is non singular and is an Anosov flow. It follows that either a pseudo-Anosov flow is topologically conjugate to a suspension Anosov flow, or any immersed incompressible torus can be realized as a free homotopy from a closed orbit of the flow to itself. The key tool is an analysis of group actions on non-Hausdorff trees, also known as R-order trees – we produce an invariant axis in the free action case. An application of these results is the following: suppose the manifold has an R-covered foliation transverse to a pseudo-Anosov flow. If the flow is not an R-covered Anosov flow, then it follows that the manifold is atoroidal.