A cotangent fibre generates the Fukaya category

TL;DR

This paper proves that the algebra of chains on the based loop space fully captures the derived wrapped Fukaya category of a cotangent bundle, establishing a deep link between algebraic and symplectic topology.

Contribution

It introduces a novel proof that a cotangent fibre generates the Fukaya category, utilizing a new approach connecting symplectic cohomology to loop space homology.

Findings

The algebra of chains on the based loop space recovers the Fukaya category.

A cotangent fibre generates the Fukaya category.

New methods connect symplectic cohomology with loop space homology.

Abstract

We prove that the algebra of chains on the based loop space recovers the derived (wrapped) Fukaya category of the cotangent bundle of a closed smooth orientable manifold. The main new idea is the proof that a cotangent fibre generates the Fukaya category using a version of the map from symplectic cohomology to the homology of the free loop space introduced by Cieliebak and Latschev.