关于可序性与弦猜想
On orderability and the chord conjecture
浏览论文内容
中文总结 AI 辅助
该研究为具有接触不可序性和辛化刚性的新接触流形类证明了Arnol'd弦猜想，涵盖Brieskorn流形等，还给出最小Reeb弦长度的统一上界，方法关联了Mohnke构造与接触Hofer几何。
中文摘要 AI 辅助
我们为一大类新的接触流形证明了Arnol'd的弦猜想：对于每个接触形式和每个闭合Legendrian子流形，存在一个端点在该Legendrian上的非常值Reeb弦。这类流形的特征是接触不可序性和辛化的刚性。这为Brieskorn流形、众多预量子化空间，以及在Legendrians上满足温和拓扑条件的所有预量子化空间证明了弦猜想。此外，它还为最小弦的长度提供了一个统一上界。我们的方法涉及Mohnke的构造与接触Hofer几何之间的新关联。
英文摘要
We prove Arnol'd's chord conjecture for a large new class of contact manifolds: for every contact form and every closed Legendrian submanifold there exists a non-constant Reeb chord with endpoints on the Legendrian. This class is characterized by contact non-orderability and rigidity of symplectizations. This proves the chord conjecture for Brieskorn manifolds, many prequantization spaces, and for all prequantization spaces under a mild topological condition on the Legendrians. Moreover, it provides a uniform upper bound on the length of the minimal chord. Our approach involves a new link between Mohnke's construction and contact Hofer geometry.
