论文标题
使用相对符号共同学的某些骨骼的超含量
Super-rigidity of certain skeleta using relative symplectic cohomology
论文作者
论文摘要
本文使用第二作者最近研究的相对符号共同体，以了解符号歧管的紧凑子集的刚性现象。作为应用程序，我们考虑了Calabi-yau simplectic歧管$ m $中的一个符号交叉分裂，其补充是liouville歧管。我们表明，对于精心挑选的liouville结构，作为$ m $的子集的骨架具有类似于Entov-Polterovich超重亚群的强刚度。一路上，我们通过引入产品和单元来扩展相对符号共同体的工具包。我们还开发了我们所谓的fukaya Trick，涉及在添加Liouville项圈下具有接触类型边界的子集的相对符号共同共同体的行为。
This article uses relative symplectic cohomology, recently studied by the second author, to understand rigidity phenomena for compact subsets of symplectic manifolds. As an application, we consider a symplectic crossings divisor in a Calabi-Yau symplectic manifold $M$ whose complement is a Liouville manifold. We show that, for a carefully chosen Liouville structure, the skeleton as a subset of $M$ exhibits strong rigidity properties akin to super-heavy subsets of Entov-Polterovich. Along the way, we expand the toolkit of relative symplectic cohomology by introducing products and units. We also develop what we call the contact Fukaya trick, concerning the behaviour of relative symplectic cohomology of subsets with contact type boundary under adding a Liouville collar.
