Generalizations of the Bonatti–Langevin example of Anosov flow and their classification up to topological equivalence
Generalizations of the Bonatti–Langevin example of Anosov flow and their classification up to topological equivalence
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DOI：
10.4310/cag.1998.v6.n4.a5
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发表时间：
1998
影响因子：
0.7
通讯作者：
Thierry Barbot
中科院分区：
文献类型：
--
作者：
Thierry Barbot
本文给出了某些3维流形上的Anosov流的一个完全分类，直至拓扑等价。这类流形是将两穿孔保护平面上的非平凡圆丛沿着其两个边界分支胶合而成的可定向流形。我们特别表明，大多数这些流形，那些不是圆丛承认一个非R-覆盖Anosov流横截环面。这些特殊的Anosov流是Bonatti-Langevin例子的自然推广，并且是通过对这个例子进行Goodman手术获得的。另外，我们得到了已知的第一个同时容纳R-覆盖和非R-覆盖Anosov流的3-流形的例子。
We give a complete classification of the Anosov flows on certain 3manifolds up to topological equivalence. These manifolds are the orientable ones obtained by glueing the non-trivial circle bundle over the two-punctured protective plane along its two boundary components. We show in particular that most of these manifolds those which are not circle bundles admit a non R-covered Anosov flow transverse to a torus. These particular Anosov flows are natural generalizations of the Bonatti-Langevin's example, and are obtained by Goodman's surgeries performed on this example. By the way, we get the first known examples of 3-manifold admitting at the same time R-covered and non R-covered Anosov flows.