论文标题
叶式开放书籍
Foliated Open Books
论文作者
论文摘要
本文在其边界上介绍了一种新型的开放式书籍分解，该触点是三个manifold的三个manifold，其中具有指定的特征叶子$ \ MATHCAL {F}_ξ$。这些\ textit {foliated Open Books}提供了一种比现有模型的凸面边界的接触歧管的更精细的工具，因为边界叶面的数据比划分集更大。除了建立有关叶面开放书籍的独特性和存在的基本结果外，我们还仔细研究了它们与本田 - 卡兹兹·马蒂（Honda-Kazez-Matic）介绍的部分开放书籍的关系。 Folieding Open Books具有用户友好的切割和粘合特性，它们自然而然地是作为封闭三元人的古典开放书籍的子手机。我们定义了三个版本的叶面开放书籍（嵌入式，摩尔斯和摘要），并证明了这些模型的等效性以及giroux信函，该信函表征了与固定三重$（M，ξ，\ Mathcal {f}）相关的叶面开放书籍。
This paper introduces a new type of open book decomposition for a contact three-manifold with a specified characteristic foliation $\mathcal{F}_ξ$ on its boundary. These \textit{foliated open books} offer a finer tool for studying contact manifolds with convex boundary than existing models, as the boundary foliation carries more data than the dividing set. In addition to establishing fundamental results about the uniqueness and existence of foliated open books, we carefully examine their relationship with the partial open books introduced by Honda-Kazez-Matic. Foliated open books have user-friendly cutting and gluing properties, and they arise naturally as submanifolds of classical open books for closed three-manifolds. We define three versions of foliated open books (embedded, Morse, and abstract), and we prove the equivalence of these models as well as a Giroux Correspondence which characterizes the foliated open books associated to a fixed triple $(M, ξ, \mathcal{F})$.
