English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Let   L   be a Lagrangian submanifold in a symplectic vector space which is closed, oriented and spin. Using virtual fundamental chains of moduli spaces of nonconstant pseudo‐holomorphic disks with boundaries on   L  , one can define a Maurer–Cartan element of a Lie bracket operation in string topology (the loop bracket) defined at chain level. This observation is due to Fukaya, who also pointed out its important consequences in symplectic topology. The goal of this paper is to work out details of this observation. Our argument is based on a string topology chain model previously introduced by the author, and the theory of Kuranishi structures on moduli spaces of pseudo‐holomorphic disks, which has been developed by Fukaya–Oh–Ohta–Ono.

Chain level loop bracket and pseudo‐holomorphic disks