On the wrapped Fukaya category and based loops

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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Published 21 March 2012