Differential forms, Fukaya A algebras, and Gromov-Witten axioms

Jake P. Solomon, Sara B. Tukachinsky

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Consider the differential forms A(L) on a Lagrangian submanifold L ⊂ X. Following ideas of Fukaya-Oh-Ohta-Ono, we construct a family of cyclic unital curved A structures on A(L), parameterized by the cohomology of X relative to L. The family of A structures satisfies properties analogous to the axioms of GromovWitten theory. Our construction is canonical up to A 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.

Original languageAmerican English
Pages (from-to)927-994
Number of pages68
JournalJournal of Symplectic Geometry
Volume20
Issue number4
DOIs
StatePublished - 2022

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