#### Volume 18, issue 1 (2018)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Other MSP Journals
The closed-open string map for $S^1$–invariant Lagrangians

### Dmitry Tonkonog

Algebraic & Geometric Topology 18 (2018) 15–68
##### 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 nonformality results for real Lagrangians in projective spaces and other toric varieties; a particularly basic example is that the equatorial circle on the $2\phantom{\rule{0.3em}{0ex}}$–sphere carries a nonformal Fukaya ${A}_{\infty }$ algebra in characteristic $2$.

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/agt

We have not been able to recognize your IP address 18.212.239.56 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.

##### Keywords
circle action, Lagrangian submanifold, Floer homology, closed-open map, Fukaya category, split-generation, formality
##### Mathematical Subject Classification 2010
Primary: 53D37, 53D40, 57R58
Secondary: 53D45