发表机构
Stanford University; The Hebrew University of Jerusalem; Koç University（斯坦福大学; 耶路撒冷希伯来大学; 科奇大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为闭辛流形中每个紧子集构造带支撑的 Fukaya 范畴，通过加速数据的完备望远镜计算态射复形，并证明 Mayer–Vietoris 下降定理。
AI 中文摘要
我们为闭辛流形 $M$ 的每个紧子集 $K$ 关联一个 $A_\infty$-范畴 $\Fuk_K$，称为支撑在 $K$ 上的 Fukaya 范畴。其对象是带有适当装饰的同伦无阻碍的整体 Lagrangian 子流形。对 $K$ 的依赖性通过态射复形来体现，这些复形可由与 $K$ 的加速数据相关的完备望远镜计算。特别地，对于与 $K$ 不相交的 Lagrangian，这些态射复形为零。当 $K=M$ 时，这恢复了通常的同伦无阻碍对象的 Fukaya 范畴。这些范畴在紧子集的包含下具有限制函子。我们证明了弱对合覆盖的 Mayer–Vietoris 下降定理。该构造在 Novikov 环上进行，并在经典横截性方法适用时得以建立。
英文摘要
We associate to each compact subset $K$ of a closed symplectic manifold $M$ an $A_\infty$-category $\Fuk_K$, called the Fukaya category with support on $K$. The objects are tautologically unobstructed global Lagrangians endowed with appropriate decorations. The dependence on $K$ is detected by the morphism complexes which can be computed by completed telescopes associated with acceleration data for $K$. In particular, these vanish for Lagrangians disjoint of $K$. For $K=M$ this recovers the usual Fukaya category of tautologically unobstructed objects. These categories admit restriction functors under inclusions of compact subsets. We prove a Mayer--Vietoris descent theorem for weakly involutive covers. The construction is carried out over the Novikov ring and is established whenever classical transversality methods apply.
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