论文标题
紧密接触结构的Thurston Norm和Euler类
Thurston norm and Euler classes of tight contact structures
论文作者
论文摘要
比尔·瑟斯顿（Bill Thurston）证明，双曲线3个manifolds的绷紧叶子最多具有欧拉类别的规范，并猜测，任何与一个的积分二数式共同学等等相等的第二个共同体学类别都可以实现为某些拉紧叶子的欧拉类。第二作者与David Gabai的联合作品的最新工作对此猜想进行了反述。由于每当绷紧的叶子繁殖时就存在紧密的接触结构，而且其欧拉类也最多也有一个规范，因此自然要问欧拉一类猜想是否对于紧密的接触结构可能仍然是正确的。在此简短说明中，我们表明，[YAZ20]中先前构造的针对欧拉的尤拉尔类别的反示例已被实现为紧密接触结构的欧拉类。这为Euler一级的猜想提供了一些证据，以实现紧密的接触结构。
Bill Thurston proved that taut foliations of hyperbolic 3-manifolds have Euler classes of norm at most one, and conjectured that any integral second cohomology class of norm equal to one is realised as the Euler class of some taut foliation. Recent work of the second author, joint with David Gabai, has produced counterexamples to this conjecture. Since tight contact structures exist whenever taut foliations do and their Euler classes also have norm at most one, it is natural to ask whether the Euler class one conjecture might still be true for tight contact structures. In this short note, we show that the previously constructed counterexamples for Euler classes of taut foliations in [Yaz20] are in fact realised as Euler classes of tight contact structures. This provides some evidence for the Euler class one conjecture for tight contact structures.
