Goodman手术与射影Anosov流
Goodman surgery and projectively Anosov flows
AI总结：
本文将Goodman手术推广至射影Anosov流范畴，，证明了任何接触Anosov流均可通过手术构造新流，并在双曲3-流形上生成新例子，同时将双接触手术与经典接触手术关联并推导出紧性结果。
摘要：
我们引入了Goodman手术在射影Anosov流范畴中的推广。该构造沿着一个同时为支撑双接触结构的Legendrian和横截的结进行。如果该流是Anosov的，存在一类特定的支撑双接触结构，它们诱导满足Barbot双曲性判据的Lorentz度量。Foulon和Hasselblatt通过从测地流进行手术构造了新的接触Anosov流。我们推广了他们的结果，证明了在任何接触Anosov流中，存在一族Legendrian结，可通过手术构造新的接触Anosov流。在Anosov流范畴之外，我们在双曲3-流形上生成了射影Anosov流的新例子。这些流包含亏格g>0的不变子流形。我们还给出了一些在接触几何中的应用：我们用经典的接触-Legendrian手术和允许-不允许的横截手术来解释双接触手术，并推导出了一些关于接触和横截手术的（超）紧性结果。
英文摘要：
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.
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