The closed-open string map for $S^1$-invariant Lagrangians
Symplectic Geometry
2018-01-23 v2
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.
Cite
@article{arxiv.1504.01621,
title = {The closed-open string map for $S^1$-invariant Lagrangians},
author = {Dmitry Tonkonog},
journal= {arXiv preprint arXiv:1504.01621},
year = {2018}
}
Comments
40 pages, 8 figures. v2: fixed a missing sign in Thm 1.7, other minor improvements; accepted version