2006/04/18 by David Nadler, Nadler, David, Eric Zaslow +1 · 4 citations
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.math/0604379
openalex publication_date 2006/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Tw Fuk(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 Tw Fuk(T^*X) as an A_∞-category. Taking cohomology gives an embedding of the corresponding derived categories.