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arXiv · 1608.01304

Differential forms, Fukaya $A_\infty$ algebras, and Gromov-Witten axioms

Jake P. Solomon·Sara B. Tukachinsky
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Abstract

Consider the differential forms $A^*(L)$ on a Lagrangian submanifold $L \subset X$. Following ideas of Fukaya-Oh-Ohta-Ono, we construct a family of cyclic unital curved $A_\infty$ structures on $A^*(L),$ parameterized by the cohomology of $X$ relative to $L.$ The family of $A_\infty$ structures satisfies properties analogous to the axioms of Gromov-Witten theory. Our construction is canonical up to $A_\infty$ pseudoisotopy. We work in the situation that moduli spaces are regular and boundary evaluation maps are submersions, and thus we do not use the theory of the virtual fundamental class.

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Jake P. Solomon, Sara B. Tukachinsky. 2023-03-26. Differential forms, Fukaya $A_\infty$ algebras, and Gromov-Witten axioms. https://doi.org/10.4310/jsg.2022.v20.n4.a5

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