论文标题
弯曲的分支表面，手术和地球流动
Veering branched surfaces, surgeries, and geodesic flows
论文作者
论文摘要
我们介绍了旋转的分支表面，作为研究转向三角形的双重方法。然后，我们讨论一些有关转向分支表面的外科手术。使用这些，我们提供了一些旋转的分支表面的明确构造，其双重旋转三角剖分对应于负弯曲的表面的地球流量。我们在（i）蒙特西诺斯链接的补充上构建了这些弯曲的分支表面，其双支封面是单位切线的分支弯曲的弯曲的圆柱状的单位切线，（ii）在地理位置不及格的情况下（$ n s $ n s $ n s yne triple atsectiral-n of），在单位切线中填充单位切线的完整填充物的完整升力补充。作为应用程序，这提供了在负弯曲表面上的地理流量的明确马尔可夫分区。在附录中，我们通过表征没有完美拟合的情况来表征对应于测量流的弯曲的三角剖分的钻孔单元切线束。
We introduce veering branched surfaces as a dual way of studying veering triangulations. We then discuss some surgical operations on veering branched surfaces. Using these, we provide explicit constructions of some veering branched surfaces whose dual veering triangulations correspond to geodesic flows of negatively curved surfaces. We construct these veering branched surfaces on (i) complements of Montesinos links whose double branched covers are unit tangent bundles of negatively curved orbifolds, and (ii) complements of full lifts of filling geodesics in unit tangent bundles of negatively curved surfaces, when the geodesics have no triple intersections and have ($n \geq 4$)-gons as complementary regions. As an application, this provides explicit Markov partitions of geodesic flows on negatively curved surfaces. In an appendix, we classify the drilled unit tangent bundles which admit a veering triangulation corresponding to a geodesic flow, by characterizing when there are no perfect fits.
