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

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
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 $2$.

##### 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
##### Publication
Revised: 19 May 2017
Accepted: 11 June 2017
Published: 10 January 2018
##### Authors
 Dmitry Tonkonog Department of Pure Mathematics and Mathematical Statistics University of Cambridge Cambridge United Kingdom