Fukaya's work on Lagrangian embeddings

TL;DR

This paper explains how string topology techniques are applied to study Lagrangian embeddings in symplectic manifolds, highlighting Fukaya's contributions in this area.

Contribution

It provides an expository overview of Fukaya's work connecting string topology with Lagrangian embeddings in symplectic geometry.

Findings

String topology offers tools for understanding Lagrangian embeddings.

Fukaya's methods link algebraic topology with symplectic geometry.

Applications include new insights into the structure of Lagrangian submanifolds.

Abstract

This is an expository account of some applications of string topology to the study of Lagrangian embeddings into symplectic manifolds, originally due to Fukaya, which was written as a contribution to a book on free loop spaces.