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

Abstract

We show that the cardinality of the transverse intersection of two compact exact Lagrangian submanifolds in a cotangent bundle is bounded from below by the dimension of the Hom space of sheaf quantizations of the Lagrangians in Tamarkin's category. Our sheaf-theoretic method can also deal with clean and degenerate Lagrangian intersections.