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

## TL;DR

This paper establishes a lower bound on the number of intersection points of two compact exact Lagrangian submanifolds in a cotangent bundle using sheaf quantization, extending to degenerate cases.

## Contribution

It introduces a sheaf-theoretic approach to bound Lagrangian intersections, including clean and degenerate cases, via Tamarkin's category.

## Key findings

- Lower bound on intersection cardinality via sheaf Hom spaces
- Applicable to clean and degenerate Lagrangian intersections
- Bridges symplectic topology and sheaf theory

## 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.