Each closed exact Lagrangian gives a finite-dimensional dg-module over the Chekanov-Eliashberg algebra, and Lagrangian Floer cohomology is recovered as derived Hom between such modules.
Covariantly functorial wrapped Floer theory on Liouville sectors
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We introduce a class of Liouville manifolds with boundary which we call Liouville sectors. We define the wrapped Fukaya category, symplectic cohomology, and the open-closed map for Liouville sectors, and we show that these invariants are covariantly functorial with respect to inclusions of Liouville sectors. From this foundational setup, a local-to-global principle for Abouzaid's generation criterion follows.
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Representations of the Chekanov-Eliashberg algebra from closed exact Lagrangians I
Each closed exact Lagrangian gives a finite-dimensional dg-module over the Chekanov-Eliashberg algebra, and Lagrangian Floer cohomology is recovered as derived Hom between such modules.