A cotangent fibre generates the Fukaya category

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.

arXiv comment40 pages, 10 figures. Minor changes. Final version to appear in Advances in Mathematics