Foliations, topology and geometry of 3-manifolds: R-covered foliations and transverse pseudo-Anosov flows
Foliations, topology and geometry of 3-manifolds: R-covered foliations and transverse pseudo-Anosov flows
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3 流形的叶状结构、拓扑和几何形状：R 覆盖的叶状结构和横向伪阿诺索夫流
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发表时间：
2002
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通讯作者：
Sérgio R. Fenley
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作者：
Sérgio R. Fenley
摘要。我们分析了3流形上叶形的拓扑和几何性质。我们考虑了3流形中r覆盖叶理的横向结构，其中r覆盖意味着在泛盖中叶理的叶空间是Hausdorff。如果流形是非球面的，我们证明流形中存在不可压缩环面；或者存在横向伪阿诺索夫流。由此可见，具有r覆盖叶的流形满足弱双曲化猜想。
Abstract. We analyse the topological and geometrical behavior of foliations on 3-manifolds. We consider the transverse structure of an R-covered foliation in a 3-manifold, where R-covered means that in the universal cover the leaf space of the foliation is Hausdorff. If the manifold is aspherical we prove that either there is an incompressible torus in the manifold; or there is a transverse pseudo-Anosov flow. It follows that manifolds with R-covered foliations satisfy the weak hyperbolization conjecture.