We show that any two birational projective Calabi-Yau manifolds have isomorphic small quantum cohomology algebras after a certain change of Novikov rings. The key tool used is a version of an algebra called symplectic cohomology, which is constructed using Hamiltonian Floer cohomology. Morally, the idea of the proof is to show that both small quantum products are identical deformations of symplectic cohomology of some common open affine subspace. Part of the proof uses the fact that subvarieties of positive codimension are stably displaceable.

中文翻译：

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双有理 Calabi-Yau 流形具有相同的小量子积

我们证明任何两个双有理射影 Calabi-Yau 流形在 Novikov 环发生一定变化后都具有同构的小量子上同调代数。使用的关键工具是一种称为辛上同调的代数版本，它是使用哈密顿 Floer 上同调构建的。从道德上讲，证明的想法是表明两个小量子乘积是某些公共开放仿射子空间的辛上同调的相同变形。部分证明使用了正余维的子变体是稳定可置换的这一事实。