Journal of Symplectic Geometry

Volume 10 (2012)

Number 1

On the wrapped Fukaya category and based loops

Pages: 27 – 79

DOI: http://dx.doi.org/10.4310/JSG.2012.v10.n1.a3

Author

Mohammed Abouzaid

Abstract

Given an exact relatively Pin Lagrangian embedding $Q \subset M$, we construct an $A^8$ 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 $A^8$ 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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