On symplectic fillings of spinal open book decompositions I: Geometric constructions
On symplectic fillings of spinal open book decompositions I: Geometric constructions
复制标题
关于脊椎开书分解的辛填充 I：几何构造
DOI：
--
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
C. Wendl
中科院分区：
文献类型：
--
作者：
S. Lisi;Jeremy Van Horn;C. Wendl
接触流形上的脊椎开书分解是自然存在的支撑开书的概括，例如在任何具有边界的致密定向表面上具有 Lefschetz 纤维的辛填充的边界上。在这个由两部分组成的系列文章的第一篇文章中，我们介绍了将脊柱开放书与 Lefschetz 纤维上的接触结构和辛或 Stein 结构相关的基本概念，从而定义了一种新的辛协调结构，称为脊柱去除手术，它概括了 Eliashberg、Gay-Stipsicz 和第三作者之前的结构。作为一种应用，脊柱去除产生了一类非强（有时不是弱）辛可填充的接触流形的新示例。本文还为第二部分要证明的定理奠定了几何基础，其中使用全纯曲线对接触 3 流形的辛填充和 Stein 填充进行分类，该接触 3 流形接纳一本带有平面页面的书脊打开的书。
A spinal open book decomposition on a contact manifold is a generalization of a supporting open book which exists naturally e.g. on the boundary of a symplectic filling with a Lefschetz fibration over any compact oriented surface with boundary. In this first paper of a two-part series, we introduce the basic notions relating spinal open books to contact structures and symplectic or Stein structures on Lefschetz fibrations, leading to the definition of a new symplectic cobordism construction called spine removal surgery, which generalizes previous constructions due to Eliashberg, Gay-Stipsicz and the third author. As an application, spine removal yields a large class of new examples of contact manifolds that are not strongly (and sometimes not weakly) symplectically fillable. This paper also lays the geometric groundwork for a theorem to be proved in part II, where holomorphic curves are used to classify the symplectic and Stein fillings of contact 3-manifolds admitting a spinal open book with a planar page.
影响因子：
0.9
作者：
Lisi S
通讯作者：
Lisi S
打开的书和温斯坦猜想
影响因子：
0.7
作者：
M. Dörner;H. Geiges;K. Zehmisch
通讯作者：
K. Zehmisch