arXiv 2406.086932024-06-12math.SG

无穷内积与开 Gromov–Witten 不变量

Infinity inner products and open Gromov--Witten invariants

Sebastian Haney

备注：: 42 pages, 11 figures

阅读 PDF

arXiv 页面 ↗HTML 原文 ↗

AI总结：

本文在珍珠模型中利用弱化的严格循环配对与循环开–闭映射，定义了任意特征零域上 Novikov 环取值的 OGW 势，并与已有构造一致。

摘要：

开 Gromov–Witten（OGW）势是一个函数，其定义域为闭辛流形中闭 Lagrangian 子流形上的弱边界上链集合，取值于 Novikov 环。现有 OGW 势的定义假定 Novikov 环的基域为 $\mathbb{R}$ 或 $\mathbb{C}$。本文在 Lagrangian Floer 理论的珍珠模型中给出 OGW 势的另一种定义，使该不变量取值于任意特征零域上的 Novikov 环。我们在简化的正则性假设下工作；例如，任何单调 Lagrangian 子流形都满足这些假设。我们的 OGW 势通过对弯曲 $A_{\infty}$-代数上严格循环配对作适当弱化来定义，这可视为一种真 Calabi–Yau 结构。该结构通过在珍珠 Lagrangian Floer 上链复形上构造一种循环开–闭映射得到。我们还说明了该构造在 de Rham 上同调中的类似形式，并证明它恢复了 Solomon 和 Tukachinsky 所构造的 OGW 势。

英文摘要：

The open Gromov--Witten (OGW) potential is a function from the set of weak bounding cochains on a closed Lagrangian in a closed symplectic manifold to the Novikov ring. Existing definitions of the OGW potential assume that the ground field of the Novikov ring is either $\mathbb{R}$ or $\mathbb{C}$. In this paper, we give an alternate definition of the OGW potential in the pearly model for Lagrangian Floer theory which yields an invariant valued in the Novikov ring over any field of characteristic zero. We work under simplifying regularity hypotheses which are satisfied, for instance, by any monotone Lagrangian. Our OGW potential is defined in terms of an appropriate weakening of a strictly cyclic pairing on a curved $A_{\infty}$-algebra, which can be thought of as a version of a proper Calabi--Yau structure. Such a structure is obtained by constructing a version of the cyclic open-closed map on the pearly Lagrangian Floer cochain complex. We also explain an analogue of our construction in de Rham cohomology, and show that it recovers the OGW potential constructed by Solomon and Tukachinsky.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

AI总结：

摘要：

英文摘要：

相关论文