This paper uses relative symplectic cohomology, recently studied by Varolgunes, 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 superheavy 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 behavior of relative symplectic cohomology of subsets with contact type boundary under adding a Liouville collar.

本文使用最近由 Varolgunes 研究的相对辛上同调来理解辛流形的紧子集的刚性现象。作为一个应用，我们考虑 Calabi–Yau 辛流形中的辛交叉因数$米$其补集是刘维尔流形。我们表明，对于精心选择的 Liouville 结构，骨架作为$米$表现出类似于 Entov-Polterovich 的超重子集的强刚性特性。在此过程中，我们通过引入乘积和单位来扩展相对辛上同调的工具包。我们还开发了所谓的接触 Fukaya 技巧，涉及在添加 Liouville 领下具有接触类型边界的子集的相对辛上同调行为。