Curved Fukaya algebras and the Dubrovin spectrum

Abstract

Under simplified axioms on moduli spaces of pseudo-holomorphic curves, we show that weakly unobstructed Fukaya algebras of Floer-nontrivial Lagrangians in a compact symplectic manifold must have curvature in the spectrum of an operator introduced by Dubrovin, which acts on the big quantum cohomology. We use the example of the complex Grassmannian $\mathrm{Gr}(2,4)$ to illustrate a decoupling phenomenon, where the eigenvalues of finite energy truncations become simple under explicit bulk-deformations.

30 pages, 7 figures