Constructible Sheaves and the Fukaya Category
نویسندگان
چکیده
Let X be a compact real analytic manifold, and let T ∗X be its cotangent bundle. Let Sh(X) be the triangulated dg category of bounded, constructible complexes of sheaves on X. In this paper, we develop a Fukaya A∞-category Fuk(T ∗X) whose objects are exact, not necessarily compact Lagrangian branes in the cotangent bundle. We write TwFuk(T ∗X) for the A∞-triangulated envelope of Fuk(T ∗X) consisting of twisted complexes of Lagrangian branes. Our main result is that Sh(X) quasi-embeds into TwFuk(T ∗X) as an A∞-category. Taking cohomology gives an embedding of the corresponding derived categories.
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