Birational Calabi-Yau manifolds have the same small quantum products

• 成果类型: Article
• 署名作者: McLean, Mark
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2020.191.2.4
• 发表日期: 2020
• 页码: 439-579
• 关键词: symplectic homology; FLOER HOMOLOGY; Invariance; rings; index; field

摘要

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.