On the wrapped Fukaya category and based loops

Details On the wrapped Fukaya category and based loops On the wrapped Fukaya category and based loops

2009-07-31

arxiv.org/abs/0907.5606v4

Mathematics

Symplectic Geometry

44 pages, 9 figures. Corrected a sign error in the comparison between wrapped Floer cohomology and the homology of the based l

Scientific paper

Given an exact relatively Pin Lagrangian embedding Q in a symplectic manifold M, we construct an A-infinity restriction functor from the wrapped Fukaya category of M to the category of modules on the differential graded algebra of chains over the based loop space of Q. If M is the cotangent bundle of Q, this functor induces an A-infinity equivalence between the wrapped Floer cohomology of a cotangent fibre and the chains over the based loop space of Q, extending a result proved by Abbondandolo and Schwarz at the level of homology.

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