发表机构
Uppsala University; TED University（乌普萨拉大学; TED大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出 Legendrian 双倍构造，推广 Courte-Ekholm 结果至任意开书，证明其有正则柔性正合 Lagrangian 填充，并由经典数据分类，且 Legendrian 悬垂是特例。
AI 中文摘要
我们定义了一种在接触流形内部构造 Legendrian 子流形的方法，该接触流形通过将开书分解页面中的一个正合 Lagrangian 填充进行双倍化而得到。这可以看作是 Courte 和 Ekholm 先前构造到任意开书的推广。这些 Legendrian 子流形被称为 Legendrian 双倍，我们证明它们允许正则的柔性正合 Lagrangian 填充，因此它们由经典数据在 Legendrian 同痕意义下完全分类。最后，我们证明由 Arikan 和作者在先前工作中定义的 Legendrian 悬垂构造——即利用 Seidel 的 Lefschetz 纤维化悬垂得到的开书页面内的 Legendrian 子流形——是一个 Legendrian 双倍。
英文摘要
We define a construction of Legendrians inside contact manifolds that arise by doubling an exact Lagrangian filling in the page of an open book decomposition. This can be seen as a generalization of a previous construction by Courte and Ekholm to arbitrary open books. These Legendrians, called Legendrian doubles, are shown to admit regular flexible exact Lagrangian fillings, and they are thus classified up to Legendrian isotopy by classical data. Finally, we show that the Legendrian suspension construction, as defined by Arikan and the author in previous work,-this is a Legendrian contained inside a page of an open book that is obtained by using Seidel's suspension of Lefschetz fibrations- is a Legendrian double.
Comments25 pages, 4 figures. Comments are welcome!
