The closed-open string map for $S^1$-invariant Lagrangians

Abstract

Given a monotone Lagrangian submanifold invariant under a loop of Hamiltonian diffeomorphisms, we compute a piece of the closed-open string map into the Hochschild cohomology of the Lagrangian which captures the homology class of the loop's orbit. Our applications include split-generation and non-formality results for real Lagrangians in projective spaces and other toric varieties; a particularly basic example is that the equatorial circle on the 2-sphere carries a non-formal Fukaya A-infinity algebra in characteristic two.

40 pages, 8 figures. v2: fixed a missing sign in Thm 1.7, other minor improvements; accepted version

References in corpus (3)

• On the Fukaya category of a Fano hypersurface in projective space
• Circle-actions, quantum cohomology, and the Fukaya category of Fano toric varieties
• Lagrangian Circle Actions

Cited by in corpus (1)

• Superfiltered $A_{\infty }$-deformations of the exterior algebra, and local mirror symmetry