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We show that the cardinality of the transverse intersection of two compactexact Lagrangian submanifolds in a cotangent bundle is bounded from below bythe dimension of the Hom space of sheaf quantizations of the Lagrangians inTamarkin's category. Our sheaf-theoretic method can also deal with clean anddegenerate Lagrangian intersections.

Compact exact Lagrangian intersections in cotangent bundles via sheaf quantization (with an appendix by Tomohiro Asano)