A cotangent fibre generates the Fukaya category

Details A cotangent fibre generates the Fukaya category A cotangent fibre generates the Fukaya category

2010-03-23

arxiv.org/abs/1003.4449v5

Mathematics

Symplectic Geometry

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

Scientific paper

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.

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