论文标题
伪anosov流的轨道等效度
Orbit equivalences of pseudo-Anosov flows
论文作者
论文摘要
我们证明了及其在封闭的3个manifolds上流动的横向Anosov和伪anosov的分类定理，直至轨道等效。 在许多情况下，在3个manifold $ m $上的流量完全取决于其（无针对性）周期性轨道的一套免费同型类别。特殊情况是在其轨道空间中具有特殊结构的流动，称为``扇形区域''；在这些情况下，一组免费的无关周期轨道的免费同型类别以及每个$π_1（m）$ - $ orbit的符号选择的其他数据，可以使orbit等价类别的不变性class of folf forp flow flow flow forp of folf forp forp forp forp colf folf forp colf Flow。 证明的框架是关于分叉平面上抽象组的\ emph {类似于Anosov的动作}的更一般结果，这表明可以从分叉的同态类型和该动作的共轭类别类别中恢复，可以从小组的哪个元素具有固定点行动的知识中恢复。 结果，我们表明，通过对轨道空间的理想边界的作用确定了Anosov的流量，并且更普遍地，更普遍地，在平面上，类似Anosov对分叉平面上的类似Anosov的动作可以通过它们在平面的边界上的作用来确定结合：在他们的理想边界上的任何共同行动在他们的理想圈子上的任何连接性都可以扩展到互联网上的相互依赖的范围。
We prove a classification theorem for transitive Anosov and pseudo-Anosov flows on closed 3-manifolds, up to orbit equivalence. In many cases, flows on a 3-manifold $M$ are completely determined by the set of free homotopy classes of their (unoriented) periodic orbits. The exceptional cases are flows with a special structure in their orbit space called a ``tree of scalloped regions"; in these cases the set of free homotopy classes of unoriented periodic orbits together with the additional data of a choice of sign for each $π_1(M)$-orbit of tree gives a complete invariant of orbit equivalence classes of flows. The framework for the proof is a more general result about \emph{Anosov-like actions} of abstract groups on bifoliated planes, showing that the homeomorphism type of the bifoliation and the conjugacy class of the action can be recovered from knowledge of which elements of the group act with fixed points. As a consequence, we show that Anosov flows are determined up to orbit equivalence by the action on the ideal boundary of their orbit spaces, and more generally that transitive Anosov-like actions on bifoliated planes are determined up to conjugacy by their actions on the plane's ideal boundary: any conjugacy between two such actions on their ideal circles can be extended uniquely to a conjugacy on the interior of the plane.
