论文标题
Goodman手术和预测的Anosov流动
Goodman surgery and projectively Anosov flows
论文作者
论文摘要
我们将古德曼手术的概括引入了投影性的Anosov流。这种结构是沿着同时进行legendrian的结和横向进行的，用于支撑双接触结构。如果流量为Anosov，则有一类特定的支持双接触结构，可诱导Lorentzian指标满足Barbot的超纤维性标准。 Foulon和Hasselblatt构建了新的接触Anosov通过大地测量流提供的手术。我们概括了他们的结果，表明在任何接触式的Anosov流中，都有一个典型结的系列，可用于通过手术来产生新的接触Anosov流。在Anosov流的范围之外，我们还为Anosov在双曲线3个manifolds上流动的新示例。这些流包含g> 0属的不变亚曼叶。我们还为接触几何形状提供了一些应用：我们用经典的接触式手术和可允许的不可接受的横向手术来解释双接触手术，并推断出一些（超级）紧密性结果以进行接触和横向手术。
We introduce a generalization of Goodman surgery to the category of projectively Anosov flows. This construction is performed along a knot that is simultaneously Legendrian and transverse for a supporting bi-contact structure. If the flow is Anosov there is a particular class of supporting bi-contact structures that induce Lorentzian metrics satisfying Barbot's criterion of hyperbolicity. Foulon and Hasselblatt construct new contact Anosov flows by surgery from a geodesic flow. We generalize their result showing that in any contact Anosov flow there is a family of Legendrian knots that can be used to produce new contact Anosov flows by surgery. Outside of the realm of Anosov flows we generate new examples of projectively Anosov flows on hyperbolic 3-manifolds. These flows contain an invariant submanifold of genus g>0. We also give some application to contact geometry: we interpret the bi-contact surgery in terms of classic contact-Legendrian surgery and admissible-inadmissible transverse surgery and we deduce some (hyper)tightness result for contact and transverse surgeries.
