We study the relationship on Weinstein domains given by Weinstein cobordism. Our main result is that any finite collection of high‐dimensional Weinstein domains with the same topology is Weinstein subdomains of a ‘maximal’ Weinstein domain also with the same topology. As applications, we construct many new exotic Weinstein structures, for example, exotic cotangent bundles containing many closed regular Lagrangians that are formally Lagrangian isotopic but not Hamiltonian isotopic and a new exotic Weinstein structure on Euclidean space. A novel feature of our construction of exotic structures is the use of results from symplectic flexibility. We also describe a similar construction in the contact setting which we use to produce ‘maximal’ contact structures and extend several existing results in low‐dimensional contact geometry to high dimensions. We prove that all contact manifolds have symplectic caps, introduce a general procedure for producing contact manifolds with many Weinstein fillings, and give a new proof of the existence of codimension two contact embeddings.

中文翻译：

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最大接触和辛结构

我们研究了由Weinstein cobordism给出的关于Weinstein域的关系。我们的主要结果是，具有相同拓扑的高维Weinstein域的任何有限集合都是具有相同拓扑的“最大” Weinstein域的Weinstein子域。作为应用程序，我们构造了许多新的奇异Weinstein结构，例如，奇异的余切束包含许多封闭的规则Lagrangian，这些Lagrangian形式上是Lagrangian同位素而不是Hamilton同位素，并且在Euclidean空间上具有新的奇异Weinstein结构。我们构造异域结构的一个新颖特征是利用辛辛那摩灵活性带来的结果。我们还在接触设置中描述了一种类似的构造，用于生成“最大”的接触结构，并将低维接触几何中的一些现有结果扩展到高维。