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.
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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.