Geodesic flow, left-handedness and templates
Geodesic flow, left-handedness and templates
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DOI：
10.2140/agt.2015.15.1525
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发表时间：
2015-01-01
影响因子：
0.7
通讯作者：
Dehornoy, Pierre
中科院分区：
文献类型：
--
作者：
Dehornoy, Pierre
我们证明了对每一个（2，q，infinity）型双曲轨道折叠和每一个（2，3，4g + 2）型轨道折叠，单位切丛上的测地流是左手的.这意味着由每个周期轨道的集合形成的链路（i）界定测地线流的Birkhoff截面，并且（ii）是纤维链路。我们也证明了类似的结果与任何平坦度量的环面。我们还观察到，自然延伸的猜想任意双曲曲面（非平凡的同源性）是假的。
We establish that for every hyperbolic orbifold of type (2, q, infinity) and for every orbifold of type (2, 3, 4g + 2), the geodesic flow on the unit tangent bundle is left handed. This implies that the link formed by every collection of periodic orbits (i) bounds a Birkhoff section for the geodesic flow, and (ii) is a fibered link. We also prove similar results for the torus with any flat metric. We also observe that the natural extension of the conjecture to arbitrary hyperbolic surfaces (with non-trivial homology) is false.