Quasigeodesic Anosov flows and homotopic properties of flow lines
Quasigeodesic Anosov flows and homotopic properties of flow lines
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DOI：
10.4310/jdg/1214456224
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发表时间：
1995
影响因子：
2.5
通讯作者：
Sérgio R. Fenley
中科院分区：
文献类型：
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作者：
Sérgio R. Fenley
当所有流线在相对同伦类中都能有效地测量距离时，一个非奇异流是拟奇异流。我们分析了具有负弯曲基本群的三维流形中的拟奇异Anosov流。我们证明了稳定的和不稳定的叶层到泛覆盖的升力是具有分枝的叶层，即它们具有非Hausdorff叶空间。此外，任何分支都与流形中的流的自由同伦闭轨有关，并且存在有限多个这样的分支叶，直到覆盖平移。利用这一点，我们证明了泛盖中稳定叶和不稳定叶的极限集不可能是Jordan曲线，也不可能是整个球面。用自由同伦轨道刻画了叶的理想点的识别。最后，对于这类流形中的任何Anosov流，我们证明了对于足够大的K，存在无数个(其中无穷多个是闭的)Kquasigeodec轨道。关键的工具是自由同伦闭轨的分析，它对于一般的Anosov流是完全刻画的。
A nonsingular flow is quasigeodesic when all flow lines are efficient in measuring distances in relative homotopy classes. We analyze quasigeodesic Anosov flows in 3-manifolds which have negatively curved fundamental group. We prove that the lifts of the stable and unstable foliations to the universal cover are foliations with branching, that is, they have non-Hausdorff leaf space. Furthermore any branching is associated to freely homotopic closed orbits of the flow in the manifold and there are finitely many such branching leaves up to covering translations. Using this we prove that the limit sets of the stable and unstable leaves in the universal cover cannot be Jordan curves nor the whole sphere. Identifications of ideal points of leaves are also described using freely homotopic orbits. Finally, for any Anosov flow in such manifolds, we prove the existence of uncountably many (infinitely many of which are closed) Kquasigeodesic orbits for K big enough. The key tool is the analysis of freely homotopic closed orbits, which are completely characterized for general Anosov flows.