焦点-焦点加法图沉浸在

arXiv - MATH - Symplectic Geometry Pub Date : 2024-09-16 DOI:arxiv-2409.10377

Mohammed Abouzaid, Nathaniel Bottman, Yunpeng Niu

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引用次数: 0

摘要

对于具有奇异拉格朗日纤维截面的交点 4-manifold $M$，局部哈密顿流给出的自然纤维加法在规则点上定义明确。我们证明，在奇点是焦点-焦点类型的情况下，相应加法图的闭包是 $(M \times M)^- \timesM$ 中拉格朗日浸入的图像，并研究了它的几何性质。我们得出这一结果的主要动机是在这种amanifold 的 Fukaya 范畴上构造了一个对称单环结构。

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The focus-focus addition graph is immersed

For a symplectic 4-manifold $M$ equipped with a singular Lagrangian fibration with a section, the natural fiberwise addition given by the local Hamiltonian flow is well-defined on the regular points. We prove, in the case that the singularities are of focus-focus type, that the closure of the corresponding addition graph is the image of a Lagrangian immersion in $(M \times M)^- \times M$, and we study its geometry. Our main motivation for this result is the construction of a symmetric monoidal structure on the Fukaya category of such a manifold.

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arXiv - MATH - Symplectic Geometry

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