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arXiv · 2411.14657

Fukaya Algebra over $\mathbb{Z}$

Mohamad Rabah
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Abstract

Given a closed, connected, relatively-spin Lagrangian submanifold in a closed symplectic manifold, we associate to it a curved, gapped, filtered, $A_{n, K}$-algebra over the Novikov ring with integer coefficients, which we extend to an $A_\infty$-algebra. To illustrate our framework, we give a proof of the Quantum Lefschetz Hyperplane Theorem in the K$\ddot a$hler case, and associate virtual fundamental classes to the moduli spaces used in local Gromov-Witten theory, in the symplectic case.

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Mohamad Rabah. 2024-11-22. Fukaya Algebra over $\mathbb{Z}$. https://arxiv.org/abs/2411.14657

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